Set Up
R Code
#packages we need for this code file
library(ggplot2)
library(mgcv)
library(lubridate)
library(zoo)
library(tidyverse)
library(dplyr)
library(DHARMa)
library(mgcViz)
library(extrafont)
library(arm)
loadfonts()
library(stargazer)
library(ellipse)
library(dotwhisker)
library(countreg)
#define functions we will need for analysis
#expit function
expit<-function(x){
return(exp(x)/(1 + exp(x)))
}
#logit function
logit<-function(x){
return(log(x/(1 - x)))
}
Data
#read in data
main_analysis_data<-read.csv("./Data/full_data_set_11_29_21_unintentional.csv")
################################## set up data set ################################
#add the intervention dates and time period data
main_analysis_data$Intervention_First_Date<-as.Date(main_analysis_data$Intervention_First_Date)
main_analysis_data$Time_Period_Start<-as.Date(main_analysis_data$Time_Period_Start)
names(main_analysis_data)[which(colnames(main_analysis_data) == "sum_deaths")] <- "imputed_deaths"
################################## set up the Regions ##############################
#set up the regions according to Census: https://www.census.gov/geographies/reference-maps/2010/geo/2010-census-regions-and-divisions-of-the-united-states.html
NE.name <- c("Connecticut","Maine","Massachusetts","New Hampshire",
"Rhode Island","Vermont","New Jersey","New York",
"Pennsylvania")
MW.name <- c("Indiana","Illinois","Michigan","Ohio","Wisconsin",
"Iowa","Kansas","Minnesota","Missouri","Nebraska",
"North Dakota","South Dakota")
S.name <- c("Delaware","District of Columbia","Florida","Georgia",
"Maryland","North Carolina","South Carolina","Virginia",
"West Virginia","Alabama","Kentucky","Mississippi",
"Tennessee","Arkansas","Louisiana","Oklahoma","Texas")
W.name <- c("Arizona","Colorado","Idaho","New Mexico","Montana",
"Utah","Nevada","Wyoming","Alaska","California",
"Hawaii","Oregon","Washington")
region.list <- list(
Northeast=NE.name,
Midwest=MW.name,
South=S.name,
West=W.name)
#initialize vector with "West" and then impute the other regions for the states
main_analysis_data$Region<-rep("West", nrow(main_analysis_data))
for(state in unique(main_analysis_data$State)){
if(state %in% region.list$Northeast){
main_analysis_data$Region[main_analysis_data$State == state]<-"Northeast"
}else if(state %in% region.list$Midwest){
main_analysis_data$Region[main_analysis_data$State == state]<-"Midwest"
}else if(state %in% region.list$South){
main_analysis_data$Region[main_analysis_data$State == state]<-"South"
}
}
Sandwich Estimator Code
#here, we estimate the variance-covariance matrix through the sandwich estimator
#we create a function so that we don't have to keep writing the code:
#cov_data is such that rows are state-time combinations and columns are the different policy measures
#coef_values need to be in order of the columns of cov_data
#z_value is the z-value that corresponds to the CI. We default to 95% CI so we default to 1.96
#we take p as the number of parametesr for a bias correction
compute_sd_and_CI <- function(cov_data, observed_y, coef_values, z_value = 1.96, p,
print_full_cov = FALSE){
middle_term <- matrix(0, nrow = ncol(cov_data), ncol = ncol(cov_data))
for(i in 1:nrow(cov_data)){
#sum_{s,t} (z_{s,t}z_{s,t}^T)*(y_{s,t}-z_{s,t}^T theta)^2
middle_term <- middle_term + tcrossprod(as.matrix(cov_data[i,]))*
as.numeric((observed_y[i] - t(as.matrix(cov_data[i,]))%*%coef_values)^2)
}
#(Z^T Z)^{-1}*middle_term*(Z^T Z)^{-1}
var_cov <- solve(crossprod(cov_data))%*%(middle_term)%*%solve(crossprod(cov_data))*(nrow(cov_data)/(nrow(cov_data) - p))
#we obtain the standard deviations by taking the square root of the diagonal of the variance-covariance matrix.
sd_of_coefficients <- sqrt(diag(var_cov))
#find the CI for the coefficients
lb_coef <- coef_values - z_value*(sd_of_coefficients)
ub_coef <- coef_values + z_value*(sd_of_coefficients)
return_data_set <- data.frame(lb_coef, coef_values, ub_coef, sd_coef = sd_of_coefficients)
if(print_full_cov){
return(list(return_data_set = return_data_set, var_cov = var_cov))
}else{
return(return_data_set)
}
}
Attributable Deaths Computation
attr_death_compute <- function(data, coef_data, post_tx_model = TRUE, tx_name = NULL){
attr_table <- data.frame(matrix(NA, nrow = unique(data$Time_Period_ID), ncol = 4))
for(time in unique(data$Time_Period_ID)){
#filter data to time period t
time_data <- data %>%
filter(Time_Period_ID == time)
#obtain the population
pop <- sum(time_data$population)
#obtain the estimated probability had intervention not occurred
if(post_tx_model == TRUE){
est_prob_no_int <- exp(log(time_data$prop_dead) - apply(sapply(0:39, function(k){time_data[,paste("pos_", k, "_pd", sep = "")]*
coef_data[paste("pos_", k, "_pd", sep = ""), "coef_values"]}), 1, sum))
}else{
est_prob_no_int <- exp(log(time_data$prop_dead) - time_data[tx_name]*coef_data[tx_name, "coef_values"])
}
#estimated number of OD had intervention not occurred
n_od_no_int <- pop*est_prob_no_int
#obtain LB
if(post_tx_model == TRUE){
est_prob_no_int_lb <- exp(log(time_data$prop_dead) - apply(sapply(0:39, function(k){time_data[,paste("pos_", k, "_pd", sep = "")]*
coef_data[paste("pos_", k, "_pd", sep = ""), "lb_coef"]}), 1, sum))
}else{
est_prob_no_int_lb <- exp(log(time_data$prop_dead) - time_data[tx_name]*coef_data[tx_name, "lb_coef"])
}
n_od_no_int_lb <- pop*est_prob_no_int_lb
#obtain UB
if(post_tx_model == TRUE){
est_prob_no_int_ub <- exp(log(time_data$prop_dead) - apply(sapply(0:39, function(k){time_data[,paste("pos_", k, "_pd", sep = "")]*
coef_data[paste("pos_", k, "_pd", sep = ""), "ub_coef"]}), 1, sum))
}else{
est_prob_no_int_ub <- exp(log(time_data$prop_dead) - time_data[tx_name]*coef_data[tx_name, "ub_coef"])
}
n_od_no_int_ub <- pop*est_prob_no_int_ub
attr_table[time,] <- c(time, sum(time_data$imputed_deaths) - sum(n_od_no_int),
sum(time_data$imputed_deaths) - sum(n_od_no_int_lb),
sum(time_data$imputed_deaths - n_od_no_int_ub))
}
colnames(attr_table) <- c("Time_Period", "attr_deaths", "attr_deaths_lb", "attr_deaths_ub")
attr_table
}
Event Study Data Creation
main_analysis_data$prop_dead <- main_analysis_data$imputed_deaths/main_analysis_data$population
#create the dataset for the event study to check for pre-trend analysis
time_data_int <- main_analysis_data %>%
#group by the state
group_by(State) %>%
#find the time interval ID for the intervention time
summarise(intervention_time_id = ifelse(floor_date(Intervention_First_Date, "6 months") == Time_Period_Start, Time_Period_ID, NA)) %>%
#filter out the other time periods that aren't the intervention date
filter(!is.na(intervention_time_id))
#merge the time_data_int with the main dataset
merged_main_time_data_int <- merge(main_analysis_data, time_data_int, by = "State", all.x = TRUE)
#create the columns that associate with the periods before the intervention
#the max number of periods before the intervention is determined by the maximum time period of the intervention
neg_periods_df <- sapply(1:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 1),
#the indicator for x periods before intervention is equal to 1 if the time ID of intervention minus time ID is equal to x
function(x){ifelse(merged_main_time_data_int$intervention_time_id -
merged_main_time_data_int$Time_Period_ID == x, 1, 0)})
#create the column names
colnames(neg_periods_df) <- sapply(1:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 1),
function(x){paste("neg_", x, "_pd", sep = "")})
#add in the state and time ID columns
neg_periods_df <- cbind(neg_periods_df, "State" = merged_main_time_data_int$State,
"Time_Period_ID" = merged_main_time_data_int$Time_Period_ID)
#for Hawaii, impute a 0 because it is NA right now
neg_periods_df[neg_periods_df[,"State"] == "Hawaii", 1:34] <- 0
#create the columns that associate with the periods after the intervention
#the max number of periods after the intervention is determined by the maximum Time ID minus the minus time period of the intervention
#the period 0 is associated with intervention time
pos_periods_df <- sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){ifelse(merged_main_time_data_int$Time_Period_ID -
merged_main_time_data_int$intervention_time_id == x, 1, 0)})
#create the column names
colnames(pos_periods_df) <- sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){paste("pos_", x, "_pd", sep = "")})
#add in the state and time ID columns
pos_periods_df <- cbind(pos_periods_df, "State" = merged_main_time_data_int$State,
"Time_Period_ID" = merged_main_time_data_int$Time_Period_ID)
#for Hawaii, impute a 0 because it is NA right now
pos_periods_df[pos_periods_df[,"State"] == "Hawaii", 1:40] <- 0
#merge the columns of indicators for before and after the intervention with the main analysis data to create the dataset for event study
sensitivity_anlys_event_study_data <- merge(main_analysis_data,
neg_periods_df, by = c("State", "Time_Period_ID"))
sensitivity_anlys_event_study_data <- merge(sensitivity_anlys_event_study_data,
pos_periods_df, by = c("State", "Time_Period_ID"))
#change the indicator values to numeric type
neg_1_index <- which(colnames(sensitivity_anlys_event_study_data) == "neg_1_pd")
pos_39_index <- which(colnames(sensitivity_anlys_event_study_data) == "pos_39_pd")
sensitivity_anlys_event_study_data[, neg_1_index:pos_39_index] <- apply(sensitivity_anlys_event_study_data[, neg_1_index:pos_39_index],
2, as.numeric)
OLS Model Main Analysis With Smoothed Time Effects
#compute the proportion of people who died from drug overdose
main_analysis_data$prop_dead <- main_analysis_data$imputed_deaths/main_analysis_data$population
#fit an OLS with smoothed time effects
main_analysis_model<-gam(prop_dead~ State +
s(Time_Period_ID, bs = "cr", by = as.factor(Region)) +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +
Intervention_Redefined ,
data = main_analysis_data)
summary(main_analysis_model)
##
## Family: gaussian
## Link function: identity
##
## Formula:
## prop_dead ~ State + s(Time_Period_ID, bs = "cr", by = as.factor(Region)) +
## Naloxone_Pharmacy_Yes_Redefined + Naloxone_Pharmacy_No_Redefined +
## Medical_Marijuana_Redefined + Recreational_Marijuana_Redefined +
## GSL_Redefined + PDMP_Redefined + Medicaid_Expansion_Redefined +
## Intervention_Redefined
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.018e-05 3.379e-06 20.769 < 2e-16 ***
## StateAlaska 5.159e-06 4.759e-06 1.084 0.278444
## StateArizona 1.365e-05 4.334e-06 3.149 0.001663 **
## StateArkansas -2.699e-05 4.270e-06 -6.321 3.23e-10 ***
## StateCalifornia -1.708e-05 4.759e-06 -3.590 0.000339 ***
## StateColorado -4.307e-06 4.742e-06 -0.908 0.363951
## StateConnecticut 1.529e-05 4.538e-06 3.369 0.000770 ***
## StateDelaware 2.394e-05 4.350e-06 5.504 4.21e-08 ***
## StateFlorida 1.569e-05 4.273e-06 3.671 0.000248 ***
## StateGeorgia -6.789e-06 4.272e-06 -1.589 0.112221
## StateHawaii -2.355e-05 4.668e-06 -5.044 4.98e-07 ***
## StateIdaho -7.124e-06 4.273e-06 -1.667 0.095614 .
## StateIllinois 5.370e-06 4.340e-06 1.237 0.216089
## StateIndiana 1.233e-05 4.245e-06 2.903 0.003732 **
## StateIowa -3.239e-05 4.259e-06 -7.604 4.46e-14 ***
## StateKansas -1.586e-05 4.227e-06 -3.752 0.000181 ***
## StateKentucky 5.811e-05 4.273e-06 13.600 < 2e-16 ***
## StateLouisiana 2.092e-05 4.221e-06 4.956 7.83e-07 ***
## StateMaine 7.921e-06 4.727e-06 1.676 0.093956 .
## StateMaryland -5.107e-05 4.337e-06 -11.776 < 2e-16 ***
## StateMassachusetts 2.091e-05 4.308e-06 4.854 1.30e-06 ***
## StateMichigan 2.500e-06 4.375e-06 0.571 0.567859
## StateMinnesota -3.845e-05 4.472e-06 -8.600 < 2e-16 ***
## StateMississippi -6.076e-06 4.223e-06 -1.439 0.150410
## StateMissouri 8.778e-06 4.368e-06 2.010 0.044589 *
## StateMontana -3.177e-05 4.496e-06 -7.066 2.22e-12 ***
## StateNebraska -3.791e-05 4.293e-06 -8.830 < 2e-16 ***
## StateNevada 2.944e-05 4.590e-06 6.414 1.78e-10 ***
## StateNew Hampshire 1.711e-05 4.296e-06 3.984 7.04e-05 ***
## StateNew Jersey 6.741e-06 4.347e-06 1.551 0.121163
## StateNew Mexico 4.934e-05 4.667e-06 10.572 < 2e-16 ***
## StateNew York -8.681e-06 4.375e-06 -1.984 0.047351 *
## StateNorth Carolina 1.214e-05 4.213e-06 2.882 0.003997 **
## StateNorth Dakota -4.294e-05 4.251e-06 -10.099 < 2e-16 ***
## StateOhio 4.302e-05 4.285e-06 10.040 < 2e-16 ***
## StateOklahoma 3.167e-05 4.252e-06 7.448 1.43e-13 ***
## StateOregon -2.464e-05 4.725e-06 -5.214 2.04e-07 ***
## StatePennsylvania 4.502e-05 4.277e-06 10.526 < 2e-16 ***
## StateRhode Island 1.971e-05 4.438e-06 4.442 9.43e-06 ***
## StateSouth Carolina 1.255e-05 4.247e-06 2.955 0.003168 **
## StateSouth Dakota -3.956e-05 4.272e-06 -9.260 < 2e-16 ***
## StateTennessee 3.447e-05 4.201e-06 8.204 4.21e-16 ***
## StateTexas -5.506e-06 4.269e-06 -1.290 0.197270
## StateUtah 3.340e-06 4.226e-06 0.790 0.429480
## StateVermont -1.370e-05 4.458e-06 -3.072 0.002153 **
## StateVirginia -3.785e-06 4.221e-06 -0.897 0.369967
## StateWashington -6.966e-06 4.813e-06 -1.447 0.147995
## StateWest Virginia 8.944e-05 4.274e-06 20.926 < 2e-16 ***
## StateWisconsin -1.498e-06 4.230e-06 -0.354 0.723299
## StateWyoming -3.949e-08 4.225e-06 -0.009 0.992544
## Naloxone_Pharmacy_Yes_Redefined -4.614e-06 2.766e-06 -1.668 0.095477 .
## Naloxone_Pharmacy_No_Redefined -1.572e-06 2.472e-06 -0.636 0.524742
## Medical_Marijuana_Redefined 1.229e-05 1.963e-06 6.259 4.76e-10 ***
## Recreational_Marijuana_Redefined -7.976e-06 3.125e-06 -2.552 0.010776 *
## GSL_Redefined 4.813e-06 2.023e-06 2.379 0.017465 *
## PDMP_Redefined -1.394e-05 1.581e-06 -8.815 < 2e-16 ***
## Medicaid_Expansion_Redefined 1.307e-05 1.937e-06 6.744 2.03e-11 ***
## Intervention_Redefined 4.835e-07 1.558e-06 0.310 0.756359
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(Time_Period_ID):as.factor(Region)Midwest 6.359 7.493 50.65 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)Northeast 8.045 8.752 78.69 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)South 7.759 8.600 78.15 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)West 3.471 4.324 49.80 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.831 Deviance explained = 83.8%
## GCV = 3.6721e-10 Scale est. = 3.5186e-10 n = 2000
gam.check(main_analysis_model, page = 1)
##
## Method: GCV Optimizer: magic
## Smoothing parameter selection converged after 4 iterations.
## The RMS GCV score gradient at convergence was 1.204512e-13 .
## The Hessian was positive definite.
## Model rank = 94 / 94
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(Time_Period_ID):as.factor(Region)Midwest 9.00 6.36 1.1 1
## s(Time_Period_ID):as.factor(Region)Northeast 9.00 8.04 1.1 1
## s(Time_Period_ID):as.factor(Region)South 9.00 7.76 1.1 1
## s(Time_Period_ID):as.factor(Region)West 9.00 3.47 1.1 1
#examine fitted values
summary(fitted(main_analysis_model))
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -3.777e-05 4.117e-05 6.437e-05 6.974e-05 9.082e-05 2.257e-04
hist(fitted(main_analysis_model))
plot(main_analysis_model, pages = 1)
Coefficients and 95% CI
#compute the full dataset including basis functions
full_df_w_basis_functions <- as.matrix(data.frame(predict(main_analysis_model, type = "lpmatrix")))
#estimate the 95% CI and SD
coefficient_values <- coef(main_analysis_model)
#type = "response" to get the estimated probabilities
main_analysis_sd_and_ci <- compute_sd_and_CI(full_df_w_basis_functions, main_analysis_data$prop_dead,
coefficient_values, p = ncol(full_df_w_basis_functions) - 50)
main_analysis_sd_and_ci
## lb_coef coef_values
## (Intercept) 6.550777e-05 7.018054e-05
## StateAlaska -2.655990e-06 5.159359e-06
## StateArizona 8.125098e-06 1.364861e-05
## StateArkansas -3.392878e-05 -2.699068e-05
## StateCalifornia -2.443119e-05 -1.708383e-05
## StateColorado -1.101178e-05 -4.306558e-06
## StateConnecticut 8.854097e-06 1.528886e-05
## StateDelaware 1.071282e-05 2.394408e-05
## StateFlorida 9.883990e-06 1.568719e-05
## StateGeorgia -1.230845e-05 -6.788984e-06
## StateHawaii -3.024143e-05 -2.354723e-05
## StateIdaho -1.202074e-05 -7.124159e-06
## StateIllinois -4.960886e-07 5.369827e-06
## StateIndiana 6.348464e-06 1.232618e-05
## StateIowa -3.811363e-05 -3.238749e-05
## StateKansas -2.087777e-05 -1.585840e-05
## StateKentucky 5.102376e-05 5.811102e-05
## StateLouisiana 1.523345e-05 2.091687e-05
## StateMaine 4.265523e-07 7.921034e-06
## StateMaryland -5.872730e-05 -5.107340e-05
## StateMassachusetts 1.387327e-05 2.091412e-05
## StateMichigan -2.897250e-06 2.499546e-06
## StateMinnesota -4.531672e-05 -3.845444e-05
## StateMississippi -1.277156e-05 -6.075702e-06
## StateMissouri 2.978337e-06 8.778322e-06
## StateMontana -3.826259e-05 -3.177095e-05
## StateNebraska -4.333837e-05 -3.790580e-05
## StateNevada 2.274149e-05 2.944268e-05
## StateNew Hampshire 9.678361e-06 1.711410e-05
## StateNew Jersey -7.745525e-07 6.740960e-06
## StateNew Mexico 4.190804e-05 4.933843e-05
## StateNew York -1.792963e-05 -8.681179e-06
## StateNorth Carolina 7.689417e-06 1.214193e-05
## StateNorth Dakota -4.966876e-05 -4.293578e-05
## StateOhio 2.893621e-05 4.301557e-05
## StateOklahoma 2.355597e-05 3.166583e-05
## StateOregon -3.120625e-05 -2.463765e-05
## StatePennsylvania 3.866383e-05 4.501742e-05
## StateRhode Island 1.070670e-05 1.971407e-05
## StateSouth Carolina 7.769104e-06 1.254959e-05
## StateSouth Dakota -4.500751e-05 -3.955940e-05
## StateTennessee 2.853688e-05 3.446740e-05
## StateTexas -1.335322e-05 -5.506353e-06
## StateUtah -4.126413e-06 3.339770e-06
## StateVermont -2.234625e-05 -1.369662e-05
## StateVirginia -9.085845e-06 -3.784903e-06
## StateWashington -1.411732e-05 -6.965542e-06
## StateWest Virginia 7.235479e-05 8.944156e-05
## StateWisconsin -6.668206e-06 -1.497789e-06
## StateWyoming -6.299542e-06 -3.948944e-08
## Naloxone_Pharmacy_Yes_Redefined -1.014411e-05 -4.613656e-06
## Naloxone_Pharmacy_No_Redefined -5.737075e-06 -1.572452e-06
## Medical_Marijuana_Redefined 7.611993e-06 1.228847e-05
## Recreational_Marijuana_Redefined -1.323577e-05 -7.975570e-06
## GSL_Redefined 8.576557e-07 4.812567e-06
## PDMP_Redefined -1.700621e-05 -1.394153e-05
## Medicaid_Expansion_Redefined 8.785126e-06 1.306529e-05
## Intervention_Redefined -2.710819e-06 4.835333e-07
## s(Time_Period_ID):as.factor(Region)Midwest.1 -2.716312e-05 -2.061983e-05
## s(Time_Period_ID):as.factor(Region)Midwest.2 -1.886956e-05 -1.405098e-05
## s(Time_Period_ID):as.factor(Region)Midwest.3 -6.335372e-06 -2.063002e-06
## s(Time_Period_ID):as.factor(Region)Midwest.4 1.639853e-06 6.425491e-06
## s(Time_Period_ID):as.factor(Region)Midwest.5 9.341242e-06 1.336075e-05
## s(Time_Period_ID):as.factor(Region)Midwest.6 1.627683e-05 2.073943e-05
## s(Time_Period_ID):as.factor(Region)Midwest.7 2.697822e-05 3.314070e-05
## s(Time_Period_ID):as.factor(Region)Midwest.8 4.256399e-05 5.232296e-05
## s(Time_Period_ID):as.factor(Region)Midwest.9 3.704131e-05 4.985907e-05
## s(Time_Period_ID):as.factor(Region)Northeast.1 -3.492814e-05 -2.690368e-05
## s(Time_Period_ID):as.factor(Region)Northeast.2 -2.795223e-05 -2.145908e-05
## s(Time_Period_ID):as.factor(Region)Northeast.3 -5.668466e-06 5.052780e-07
## s(Time_Period_ID):as.factor(Region)Northeast.4 -5.787646e-06 -4.993248e-08
## s(Time_Period_ID):as.factor(Region)Northeast.5 -4.689682e-06 1.391242e-06
## s(Time_Period_ID):as.factor(Region)Northeast.6 6.329001e-06 1.294496e-05
## s(Time_Period_ID):as.factor(Region)Northeast.7 3.867293e-05 4.828531e-05
## s(Time_Period_ID):as.factor(Region)Northeast.8 8.539287e-05 9.629882e-05
## s(Time_Period_ID):as.factor(Region)Northeast.9 6.552090e-05 8.026878e-05
## s(Time_Period_ID):as.factor(Region)South.1 -3.022522e-05 -2.337861e-05
## s(Time_Period_ID):as.factor(Region)South.2 -1.719691e-05 -1.253656e-05
## s(Time_Period_ID):as.factor(Region)South.3 -1.858526e-06 3.729042e-06
## s(Time_Period_ID):as.factor(Region)South.4 5.410765e-06 1.112647e-05
## s(Time_Period_ID):as.factor(Region)South.5 1.594179e-05 2.101759e-05
## s(Time_Period_ID):as.factor(Region)South.6 1.959869e-05 2.481184e-05
## s(Time_Period_ID):as.factor(Region)South.7 3.401158e-05 4.039071e-05
## s(Time_Period_ID):as.factor(Region)South.8 5.858355e-05 6.897540e-05
## s(Time_Period_ID):as.factor(Region)South.9 4.412813e-05 6.040295e-05
## s(Time_Period_ID):as.factor(Region)West.1 -1.869797e-05 -1.440514e-05
## s(Time_Period_ID):as.factor(Region)West.2 -9.832141e-06 -6.268216e-06
## s(Time_Period_ID):as.factor(Region)West.3 -3.690218e-07 3.701112e-06
## s(Time_Period_ID):as.factor(Region)West.4 8.175889e-06 1.186207e-05
## s(Time_Period_ID):as.factor(Region)West.5 1.340384e-05 1.734734e-05
## s(Time_Period_ID):as.factor(Region)West.6 1.665064e-05 2.108933e-05
## s(Time_Period_ID):as.factor(Region)West.7 1.896157e-05 2.437395e-05
## s(Time_Period_ID):as.factor(Region)West.8 2.439385e-05 3.137238e-05
## s(Time_Period_ID):as.factor(Region)West.9 2.428297e-05 3.186887e-05
## ub_coef sd_coef
## (Intercept) 7.485331e-05 2.384067e-06
## StateAlaska 1.297471e-05 3.987423e-06
## StateArizona 1.917213e-05 2.818121e-06
## StateArkansas -2.005259e-05 3.539844e-06
## StateCalifornia -9.736475e-06 3.748651e-06
## StateColorado 2.398666e-06 3.421033e-06
## StateConnecticut 2.172362e-05 3.283042e-06
## StateDelaware 3.717534e-05 6.750643e-06
## StateFlorida 2.149038e-05 2.960814e-06
## StateGeorgia -1.269519e-06 2.816053e-06
## StateHawaii -1.685303e-05 3.415408e-06
## StateIdaho -2.227577e-06 2.498256e-06
## StateIllinois 1.123574e-05 2.992814e-06
## StateIndiana 1.830390e-05 3.049856e-06
## StateIowa -2.666136e-05 2.921497e-06
## StateKansas -1.083903e-05 2.560905e-06
## StateKentucky 6.519828e-05 3.615948e-06
## StateLouisiana 2.660028e-05 2.899703e-06
## StateMaine 1.541551e-05 3.823715e-06
## StateMaryland -4.341950e-05 3.905053e-06
## StateMassachusetts 2.795498e-05 3.592274e-06
## StateMichigan 7.896342e-06 2.753467e-06
## StateMinnesota -3.159217e-05 3.501162e-06
## StateMississippi 6.201522e-07 3.416252e-06
## StateMissouri 1.457831e-05 2.959176e-06
## StateMontana -2.527930e-05 3.312066e-06
## StateNebraska -3.247323e-05 2.771721e-06
## StateNevada 3.614387e-05 3.418975e-06
## StateNew Hampshire 2.454984e-05 3.793744e-06
## StateNew Jersey 1.425647e-05 3.834445e-06
## StateNew Mexico 5.676881e-05 3.791013e-06
## StateNew York 5.672703e-07 4.718596e-06
## StateNorth Carolina 1.659443e-05 2.271688e-06
## StateNorth Dakota -3.620281e-05 3.435192e-06
## StateOhio 5.709492e-05 7.183345e-06
## StateOklahoma 3.977569e-05 4.137683e-06
## StateOregon -1.806905e-05 3.351325e-06
## StatePennsylvania 5.137102e-05 3.241630e-06
## StateRhode Island 2.872143e-05 4.595593e-06
## StateSouth Carolina 1.733007e-05 2.439021e-06
## StateSouth Dakota -3.411129e-05 2.779648e-06
## StateTennessee 4.039793e-05 3.025776e-06
## StateTexas 2.340510e-06 4.003501e-06
## StateUtah 1.080595e-05 3.809277e-06
## StateVermont -5.046981e-06 4.413079e-06
## StateVirginia 1.516039e-06 2.704562e-06
## StateWashington 1.862399e-07 3.648868e-06
## StateWest Virginia 1.065283e-04 8.717742e-06
## StateWisconsin 3.672628e-06 2.637968e-06
## StateWyoming 6.220563e-06 3.193904e-06
## Naloxone_Pharmacy_Yes_Redefined 9.167953e-07 2.821659e-06
## Naloxone_Pharmacy_No_Redefined 2.592170e-06 2.124808e-06
## Medical_Marijuana_Redefined 1.696495e-05 2.385958e-06
## Recreational_Marijuana_Redefined -2.715372e-06 2.683774e-06
## GSL_Redefined 8.767479e-06 2.017812e-06
## PDMP_Redefined -1.087685e-05 1.563614e-06
## Medicaid_Expansion_Redefined 1.734545e-05 2.183756e-06
## Intervention_Redefined 3.677886e-06 1.629772e-06
## s(Time_Period_ID):as.factor(Region)Midwest.1 -1.407655e-05 3.338411e-06
## s(Time_Period_ID):as.factor(Region)Midwest.2 -9.232397e-06 2.458461e-06
## s(Time_Period_ID):as.factor(Region)Midwest.3 2.209367e-06 2.179781e-06
## s(Time_Period_ID):as.factor(Region)Midwest.4 1.121113e-05 2.441652e-06
## s(Time_Period_ID):as.factor(Region)Midwest.5 1.738026e-05 2.050771e-06
## s(Time_Period_ID):as.factor(Region)Midwest.6 2.520204e-05 2.276838e-06
## s(Time_Period_ID):as.factor(Region)Midwest.7 3.930318e-05 3.144121e-06
## s(Time_Period_ID):as.factor(Region)Midwest.8 6.208194e-05 4.979071e-06
## s(Time_Period_ID):as.factor(Region)Midwest.9 6.267683e-05 6.539674e-06
## s(Time_Period_ID):as.factor(Region)Northeast.1 -1.887921e-05 4.094113e-06
## s(Time_Period_ID):as.factor(Region)Northeast.2 -1.496592e-05 3.312834e-06
## s(Time_Period_ID):as.factor(Region)Northeast.3 6.679022e-06 3.149869e-06
## s(Time_Period_ID):as.factor(Region)Northeast.4 5.687781e-06 2.927405e-06
## s(Time_Period_ID):as.factor(Region)Northeast.5 7.472166e-06 3.102512e-06
## s(Time_Period_ID):as.factor(Region)Northeast.6 1.956092e-05 3.375488e-06
## s(Time_Period_ID):as.factor(Region)Northeast.7 5.789768e-05 4.904272e-06
## s(Time_Period_ID):as.factor(Region)Northeast.8 1.072048e-04 5.564261e-06
## s(Time_Period_ID):as.factor(Region)Northeast.9 9.501667e-05 7.524432e-06
## s(Time_Period_ID):as.factor(Region)South.1 -1.653200e-05 3.493167e-06
## s(Time_Period_ID):as.factor(Region)South.2 -7.876207e-06 2.377730e-06
## s(Time_Period_ID):as.factor(Region)South.3 9.316611e-06 2.850800e-06
## s(Time_Period_ID):as.factor(Region)South.4 1.684217e-05 2.916176e-06
## s(Time_Period_ID):as.factor(Region)South.5 2.609339e-05 2.589692e-06
## s(Time_Period_ID):as.factor(Region)South.6 3.002500e-05 2.659775e-06
## s(Time_Period_ID):as.factor(Region)South.7 4.676984e-05 3.254660e-06
## s(Time_Period_ID):as.factor(Region)South.8 7.936725e-05 5.301965e-06
## s(Time_Period_ID):as.factor(Region)South.9 7.667777e-05 8.303480e-06
## s(Time_Period_ID):as.factor(Region)West.1 -1.011232e-05 2.190216e-06
## s(Time_Period_ID):as.factor(Region)West.2 -2.704291e-06 1.818329e-06
## s(Time_Period_ID):as.factor(Region)West.3 7.771245e-06 2.076599e-06
## s(Time_Period_ID):as.factor(Region)West.4 1.554826e-05 1.880707e-06
## s(Time_Period_ID):as.factor(Region)West.5 2.129085e-05 2.011993e-06
## s(Time_Period_ID):as.factor(Region)West.6 2.552802e-05 2.264638e-06
## s(Time_Period_ID):as.factor(Region)West.7 2.978632e-05 2.761414e-06
## s(Time_Period_ID):as.factor(Region)West.8 3.835090e-05 3.560473e-06
## s(Time_Period_ID):as.factor(Region)West.9 3.945476e-05 3.870355e-06
Event Study
Model Fitting
#create a formula for the gam model which includes the state effects, smoothed time effects, policy measures,
#the periods before the intervention (excluding 1 period and 34 periods before intervention)
#the intervention period, and the periods after the intervention
formula_event_study <- formula(paste("prop_dead ~ State +
s(Time_Period_ID, bs = 'cr', by = as.factor(Region)) +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +",
paste(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)-2),
function(x)paste("neg_", x, "_pd", sep = "")), collapse = "+"),
"+",
paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_event_study_model<-gam(formula_event_study,
data = sensitivity_anlys_event_study_data)
summary(sensitivity_anlys_event_study_model)
##
## Family: gaussian
## Link function: identity
##
## Formula:
## prop_dead ~ State + s(Time_Period_ID, bs = "cr", by = as.factor(Region)) +
## Naloxone_Pharmacy_Yes_Redefined + Naloxone_Pharmacy_No_Redefined +
## Medical_Marijuana_Redefined + Recreational_Marijuana_Redefined +
## GSL_Redefined + PDMP_Redefined + Medicaid_Expansion_Redefined +
## neg_2_pd + neg_3_pd + neg_4_pd + neg_5_pd + neg_6_pd + neg_7_pd +
## neg_8_pd + neg_9_pd + neg_10_pd + neg_11_pd + neg_12_pd +
## neg_13_pd + neg_14_pd + neg_15_pd + neg_16_pd + neg_17_pd +
## neg_18_pd + neg_19_pd + neg_20_pd + neg_21_pd + neg_22_pd +
## neg_23_pd + neg_24_pd + neg_25_pd + neg_26_pd + neg_27_pd +
## neg_28_pd + neg_29_pd + neg_30_pd + neg_31_pd + neg_32_pd +
## neg_33_pd + pos_0_pd + pos_1_pd + pos_2_pd + pos_3_pd + pos_4_pd +
## pos_5_pd + pos_6_pd + pos_7_pd + pos_8_pd + pos_9_pd + pos_10_pd +
## pos_11_pd + pos_12_pd + pos_13_pd + pos_14_pd + pos_15_pd +
## pos_16_pd + pos_17_pd + pos_18_pd + pos_19_pd + pos_20_pd +
## pos_21_pd + pos_22_pd + pos_23_pd + pos_24_pd + pos_25_pd +
## pos_26_pd + pos_27_pd + pos_28_pd + pos_29_pd + pos_30_pd +
## pos_31_pd + pos_32_pd + pos_33_pd + pos_34_pd + pos_35_pd +
## pos_36_pd + pos_37_pd + pos_38_pd + pos_39_pd
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.588e-05 4.354e-06 17.428 < 2e-16 ***
## StateAlaska 1.166e-05 6.301e-06 1.850 0.064426 .
## StateArizona 1.775e-05 4.846e-06 3.663 0.000256 ***
## StateArkansas -2.462e-05 4.547e-06 -5.414 6.98e-08 ***
## StateCalifornia -1.897e-05 5.581e-06 -3.399 0.000692 ***
## StateColorado -2.222e-07 5.135e-06 -0.043 0.965483
## StateConnecticut 1.530e-05 4.506e-06 3.395 0.000700 ***
## StateDelaware 2.987e-05 6.004e-06 4.975 7.14e-07 ***
## StateFlorida 1.139e-05 5.493e-06 2.073 0.038323 *
## StateGeorgia -1.240e-05 5.864e-06 -2.115 0.034548 *
## StateHawaii -2.639e-05 5.451e-06 -4.841 1.40e-06 ***
## StateIdaho -9.651e-07 5.658e-06 -0.171 0.864578
## StateIllinois 2.603e-06 5.048e-06 0.516 0.606170
## StateIndiana 1.431e-05 4.325e-06 3.308 0.000957 ***
## StateIowa -3.365e-05 4.593e-06 -7.326 3.52e-13 ***
## StateKansas -1.609e-05 4.200e-06 -3.830 0.000132 ***
## StateKentucky 6.135e-05 4.579e-06 13.399 < 2e-16 ***
## StateLouisiana 1.894e-05 4.647e-06 4.076 4.78e-05 ***
## StateMaine 1.067e-05 4.767e-06 2.237 0.025374 *
## StateMaryland -5.506e-05 5.120e-06 -10.754 < 2e-16 ***
## StateMassachusetts 2.174e-05 4.272e-06 5.088 3.98e-07 ***
## StateMichigan 2.888e-06 4.488e-06 0.644 0.519936
## StateMinnesota -3.812e-05 4.445e-06 -8.577 < 2e-16 ***
## StateMississippi -1.315e-06 5.276e-06 -0.249 0.803243
## StateMissouri 6.589e-06 4.545e-06 1.450 0.147278
## StateMontana -3.305e-05 4.868e-06 -6.790 1.51e-11 ***
## StateNebraska -3.434e-05 4.888e-06 -7.026 2.98e-12 ***
## StateNevada 3.027e-05 4.674e-06 6.476 1.20e-10 ***
## StateNew Hampshire 1.837e-05 4.365e-06 4.208 2.69e-05 ***
## StateNew Jersey 3.449e-06 5.099e-06 0.676 0.498916
## StateNew Mexico 5.124e-05 4.758e-06 10.771 < 2e-16 ***
## StateNew York -8.375e-06 4.344e-06 -1.928 0.054035 .
## StateNorth Carolina 1.088e-05 4.432e-06 2.454 0.014211 *
## StateNorth Dakota -3.894e-05 4.869e-06 -7.999 2.20e-15 ***
## StateOhio 3.830e-05 5.855e-06 6.541 7.88e-11 ***
## StateOklahoma 3.502e-05 4.498e-06 7.786 1.15e-14 ***
## StateOregon -2.245e-05 4.797e-06 -4.680 3.07e-06 ***
## StatePennsylvania 4.174e-05 5.463e-06 7.640 3.47e-14 ***
## StateRhode Island 2.541e-05 5.382e-06 4.722 2.51e-06 ***
## StateSouth Carolina 1.841e-05 5.762e-06 3.196 0.001418 **
## StateSouth Dakota -3.379e-05 5.961e-06 -5.668 1.67e-08 ***
## StateTennessee 3.470e-05 4.162e-06 8.336 < 2e-16 ***
## StateTexas -8.210e-06 5.292e-06 -1.551 0.121017
## StateUtah 2.925e-06 4.357e-06 0.671 0.502135
## StateVermont -1.178e-05 4.512e-06 -2.611 0.009099 **
## StateVirginia -5.799e-06 4.732e-06 -1.225 0.220576
## StateWashington -5.644e-06 4.809e-06 -1.174 0.240692
## StateWest Virginia 9.400e-05 4.909e-06 19.151 < 2e-16 ***
## StateWisconsin -3.846e-06 4.659e-06 -0.826 0.409194
## StateWyoming 1.701e-06 4.259e-06 0.399 0.689636
## Naloxone_Pharmacy_Yes_Redefined -4.335e-06 2.768e-06 -1.566 0.117412
## Naloxone_Pharmacy_No_Redefined -1.607e-06 2.476e-06 -0.649 0.516370
## Medical_Marijuana_Redefined 1.095e-05 1.987e-06 5.510 4.10e-08 ***
## Recreational_Marijuana_Redefined -8.742e-06 3.156e-06 -2.770 0.005667 **
## GSL_Redefined 6.151e-06 2.023e-06 3.041 0.002394 **
## PDMP_Redefined -1.595e-05 1.601e-06 -9.961 < 2e-16 ***
## Medicaid_Expansion_Redefined 1.342e-05 1.958e-06 6.852 9.89e-12 ***
## neg_2_pd -4.444e-07 3.819e-06 -0.116 0.907376
## neg_3_pd 2.553e-07 3.881e-06 0.066 0.947557
## neg_4_pd -3.100e-06 3.967e-06 -0.781 0.434610
## neg_5_pd -5.533e-06 4.018e-06 -1.377 0.168666
## neg_6_pd -5.831e-06 4.157e-06 -1.403 0.160816
## neg_7_pd -9.095e-06 4.228e-06 -2.151 0.031609 *
## neg_8_pd -1.185e-05 4.333e-06 -2.735 0.006290 **
## neg_9_pd -8.193e-06 4.513e-06 -1.815 0.069618 .
## neg_10_pd -8.270e-06 4.643e-06 -1.781 0.075075 .
## neg_11_pd -9.350e-06 4.789e-06 -1.952 0.051071 .
## neg_12_pd -5.952e-06 5.068e-06 -1.174 0.240420
## neg_13_pd -9.391e-06 5.195e-06 -1.808 0.070823 .
## neg_14_pd -1.067e-05 5.329e-06 -2.003 0.045343 *
## neg_15_pd -1.488e-05 5.477e-06 -2.716 0.006665 **
## neg_16_pd -1.449e-05 5.753e-06 -2.518 0.011884 *
## neg_17_pd -1.773e-05 6.081e-06 -2.915 0.003600 **
## neg_18_pd -1.867e-05 6.299e-06 -2.964 0.003079 **
## neg_19_pd -1.932e-05 6.505e-06 -2.970 0.003015 **
## neg_20_pd -2.166e-05 6.879e-06 -3.149 0.001667 **
## neg_21_pd -2.102e-05 7.336e-06 -2.865 0.004215 **
## neg_22_pd -2.126e-05 7.508e-06 -2.832 0.004678 **
## neg_23_pd -1.875e-05 7.773e-06 -2.412 0.015962 *
## neg_24_pd -2.300e-05 8.341e-06 -2.758 0.005876 **
## neg_25_pd -2.053e-05 8.492e-06 -2.417 0.015739 *
## neg_26_pd -1.630e-05 8.858e-06 -1.841 0.065848 .
## neg_27_pd -1.569e-05 9.861e-06 -1.591 0.111775
## neg_28_pd -1.508e-05 1.003e-05 -1.503 0.132989
## neg_29_pd -1.225e-05 1.059e-05 -1.157 0.247534
## neg_30_pd -1.690e-05 1.126e-05 -1.501 0.133548
## neg_31_pd -1.853e-05 1.142e-05 -1.623 0.104834
## neg_32_pd -1.878e-05 1.239e-05 -1.515 0.129881
## neg_33_pd -1.241e-05 1.572e-05 -0.789 0.430066
## pos_0_pd 2.540e-08 3.802e-06 0.007 0.994671
## pos_1_pd -1.353e-06 3.842e-06 -0.352 0.724804
## pos_2_pd 1.645e-06 3.896e-06 0.422 0.673011
## pos_3_pd -9.337e-09 3.966e-06 -0.002 0.998122
## pos_4_pd 5.733e-07 4.046e-06 0.142 0.887347
## pos_5_pd -1.838e-06 4.140e-06 -0.444 0.657198
## pos_6_pd 2.345e-07 4.255e-06 0.055 0.956048
## pos_7_pd -5.369e-07 4.380e-06 -0.123 0.902451
## pos_8_pd -1.869e-06 4.543e-06 -0.411 0.680860
## pos_9_pd -3.141e-06 4.696e-06 -0.669 0.503773
## pos_10_pd -3.393e-06 4.831e-06 -0.702 0.482512
## pos_11_pd -3.053e-06 4.997e-06 -0.611 0.541318
## pos_12_pd -2.000e-06 5.172e-06 -0.387 0.699080
## pos_13_pd -5.156e-06 5.332e-06 -0.967 0.333701
## pos_14_pd -3.669e-06 5.558e-06 -0.660 0.509167
## pos_15_pd -5.162e-06 5.766e-06 -0.895 0.370752
## pos_16_pd -6.156e-06 5.952e-06 -1.034 0.301138
## pos_17_pd -4.156e-06 6.195e-06 -0.671 0.502457
## pos_18_pd -3.494e-06 6.410e-06 -0.545 0.585741
## pos_19_pd -2.675e-06 6.587e-06 -0.406 0.684710
## pos_20_pd -3.948e-06 6.860e-06 -0.576 0.564969
## pos_21_pd -4.241e-06 7.134e-06 -0.594 0.552288
## pos_22_pd -1.785e-06 7.359e-06 -0.243 0.808345
## pos_23_pd -8.797e-07 7.620e-06 -0.115 0.908101
## pos_24_pd -4.155e-06 7.956e-06 -0.522 0.601536
## pos_25_pd -1.945e-06 8.292e-06 -0.235 0.814587
## pos_26_pd -1.574e-06 8.490e-06 -0.185 0.852925
## pos_27_pd -4.658e-06 8.717e-06 -0.534 0.593175
## pos_28_pd -1.813e-06 8.911e-06 -0.203 0.838777
## pos_29_pd -5.020e-06 9.380e-06 -0.535 0.592574
## pos_30_pd 4.239e-07 9.670e-06 0.044 0.965035
## pos_31_pd 1.238e-05 1.000e-05 1.237 0.216165
## pos_32_pd 1.023e-05 1.064e-05 0.961 0.336454
## pos_33_pd 9.607e-06 1.104e-05 0.870 0.384190
## pos_34_pd 1.713e-05 1.125e-05 1.524 0.127800
## pos_35_pd 2.667e-06 1.228e-05 0.217 0.828168
## pos_36_pd -1.436e-06 1.249e-05 -0.115 0.908516
## pos_37_pd 1.587e-05 1.391e-05 1.141 0.253901
## pos_38_pd 1.614e-05 1.694e-05 0.952 0.340977
## pos_39_pd 2.397e-05 1.720e-05 1.394 0.163614
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(Time_Period_ID):as.factor(Region)Midwest 6.802 7.892 8.249 < 2e-16 ***
## s(Time_Period_ID):as.factor(Region)Northeast 7.971 8.719 33.756 < 2e-16 ***
## s(Time_Period_ID):as.factor(Region)South 7.760 8.601 13.645 < 2e-16 ***
## s(Time_Period_ID):as.factor(Region)West 3.218 4.023 8.800 9.84e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.834 Deviance explained = 84.7%
## GCV = 3.7432e-10 Scale est. = 3.4535e-10 n = 2000
Sandwich Estimator
#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_event_study <- data.frame(predict(sensitivity_anlys_event_study_model, type = "lpmatrix"))
#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_event_study <- coef(sensitivity_anlys_event_study_model)
#type = "response" to get the estimated probabilities
sensitivity_anlys_event_study_sd_and_ci <- compute_sd_and_CI(as.matrix(full_df_w_basis_functions_sensitivity_anlys_event_study),
sensitivity_anlys_event_study_data$prop_dead,
coefficient_values_sensitivity_anlys_event_study,
p = ncol(full_df_w_basis_functions_sensitivity_anlys_event_study) - 50)
(sensitivity_anlys_event_study_sd_and_ci)
## lb_coef coef_values
## (Intercept) 7.018758e-05 7.588153e-05
## StateAlaska 2.702969e-06 1.165915e-05
## StateArizona 1.155015e-05 1.775014e-05
## StateArkansas -3.147916e-05 -2.461562e-05
## StateCalifornia -2.621282e-05 -1.896949e-05
## StateColorado -7.373523e-06 -2.222402e-07
## StateConnecticut 9.001384e-06 1.529978e-05
## StateDelaware 1.674016e-05 2.986929e-05
## StateFlorida 4.837064e-06 1.138546e-05
## StateGeorgia -1.962541e-05 -1.240243e-05
## StateHawaii -3.362101e-05 -2.638682e-05
## StateIdaho -7.178603e-06 -9.651171e-07
## StateIllinois -3.493598e-06 2.602818e-06
## StateIndiana 8.595625e-06 1.430953e-05
## StateIowa -3.926947e-05 -3.365310e-05
## StateKansas -2.077318e-05 -1.608743e-05
## StateKentucky 5.467657e-05 6.134916e-05
## StateLouisiana 1.307945e-05 1.894281e-05
## StateMaine 3.064209e-06 1.066642e-05
## StateMaryland -6.264271e-05 -5.505916e-05
## StateMassachusetts 1.487224e-05 2.173840e-05
## StateMichigan -2.245238e-06 2.888378e-06
## StateMinnesota -4.470511e-05 -3.811967e-05
## StateMississippi -9.373824e-06 -1.314824e-06
## StateMissouri 4.649449e-07 6.589117e-06
## StateMontana -3.912099e-05 -3.305272e-05
## StateNebraska -4.052068e-05 -3.434330e-05
## StateNevada 2.390005e-05 3.026966e-05
## StateNew Hampshire 1.079763e-05 1.836949e-05
## StateNew Jersey -3.652057e-06 3.448585e-06
## StateNew Mexico 4.384943e-05 5.124463e-05
## StateNew York -1.732233e-05 -8.374509e-06
## StateNorth Carolina 6.264255e-06 1.087630e-05
## StateNorth Dakota -4.679897e-05 -3.894169e-05
## StateOhio 2.420983e-05 3.829869e-05
## StateOklahoma 2.743480e-05 3.501696e-05
## StateOregon -2.899092e-05 -2.245349e-05
## StatePennsylvania 3.492330e-05 4.174037e-05
## StateRhode Island 1.662438e-05 2.541168e-05
## StateSouth Carolina 1.218258e-05 1.841450e-05
## StateSouth Dakota -4.078667e-05 -3.378823e-05
## StateTennessee 2.847526e-05 3.469856e-05
## StateTexas -1.628838e-05 -8.209918e-06
## StateUtah -5.184532e-06 2.924894e-06
## StateVermont -2.046081e-05 -1.178060e-05
## StateVirginia -1.101404e-05 -5.799118e-06
## StateWashington -1.264762e-05 -5.643995e-06
## StateWest Virginia 7.736240e-05 9.400384e-05
## StateWisconsin -9.701198e-06 -3.846319e-06
## StateWyoming -4.263640e-06 1.701292e-06
## Naloxone_Pharmacy_Yes_Redefined -9.693092e-06 -4.335218e-06
## Naloxone_Pharmacy_No_Redefined -5.773398e-06 -1.607156e-06
## Medical_Marijuana_Redefined 6.354468e-06 1.094530e-05
## Recreational_Marijuana_Redefined -1.433592e-05 -8.742271e-06
## GSL_Redefined 2.180344e-06 6.150972e-06
## PDMP_Redefined -1.905469e-05 -1.594534e-05
## Medicaid_Expansion_Redefined 9.070130e-06 1.341748e-05
## neg_2_pd -5.924682e-06 -4.443708e-07
## neg_3_pd -5.431833e-06 2.553242e-07
## neg_4_pd -9.092257e-06 -3.100244e-06
## neg_5_pd -1.098886e-05 -5.532630e-06
## neg_6_pd -1.113919e-05 -5.831373e-06
## neg_7_pd -1.540913e-05 -9.094939e-06
## neg_8_pd -1.975811e-05 -1.185350e-05
## neg_9_pd -1.446516e-05 -8.192513e-06
## neg_10_pd -1.411553e-05 -8.269582e-06
## neg_11_pd -1.549125e-05 -9.349852e-06
## neg_12_pd -1.316649e-05 -5.951537e-06
## neg_13_pd -1.608167e-05 -9.391280e-06
## neg_14_pd -1.850258e-05 -1.067322e-05
## neg_15_pd -2.456176e-05 -1.487699e-05
## neg_16_pd -2.188313e-05 -1.448732e-05
## neg_17_pd -2.571926e-05 -1.772553e-05
## neg_18_pd -2.691398e-05 -1.866777e-05
## neg_19_pd -2.826921e-05 -1.931907e-05
## neg_20_pd -3.074698e-05 -2.165852e-05
## neg_21_pd -3.180203e-05 -2.101830e-05
## neg_22_pd -3.489513e-05 -2.126153e-05
## neg_23_pd -3.177972e-05 -1.874855e-05
## neg_24_pd -3.810040e-05 -2.300221e-05
## neg_25_pd -3.725609e-05 -2.052759e-05
## neg_26_pd -3.552791e-05 -1.630307e-05
## neg_27_pd -2.917577e-05 -1.568866e-05
## neg_28_pd -2.739710e-05 -1.507752e-05
## neg_29_pd -2.244514e-05 -1.224774e-05
## neg_30_pd -2.827549e-05 -1.690021e-05
## neg_31_pd -3.134989e-05 -1.852997e-05
## neg_32_pd -3.298367e-05 -1.877590e-05
## neg_33_pd -3.024011e-05 -1.240748e-05
## pos_0_pd -5.579131e-06 2.539847e-08
## pos_1_pd -7.658457e-06 -1.352591e-06
## pos_2_pd -4.646623e-06 1.644575e-06
## pos_3_pd -6.634944e-06 -9.336550e-09
## pos_4_pd -6.358173e-06 5.732680e-07
## pos_5_pd -8.633026e-06 -1.837598e-06
## pos_6_pd -7.744238e-06 2.345472e-07
## pos_7_pd -8.281404e-06 -5.369095e-07
## pos_8_pd -1.054788e-05 -1.868906e-06
## pos_9_pd -1.046480e-05 -3.140505e-06
## pos_10_pd -1.085704e-05 -3.393235e-06
## pos_11_pd -1.060797e-05 -3.053075e-06
## pos_12_pd -9.146633e-06 -1.999758e-06
## pos_13_pd -1.372242e-05 -5.156054e-06
## pos_14_pd -1.174593e-05 -3.669463e-06
## pos_15_pd -1.336103e-05 -5.162032e-06
## pos_16_pd -1.480096e-05 -6.156197e-06
## pos_17_pd -1.268278e-05 -4.155646e-06
## pos_18_pd -1.200255e-05 -3.494411e-06
## pos_19_pd -1.098053e-05 -2.674879e-06
## pos_20_pd -1.269841e-05 -3.948372e-06
## pos_21_pd -1.364231e-05 -4.240683e-06
## pos_22_pd -1.157539e-05 -1.785388e-06
## pos_23_pd -1.213957e-05 -8.797009e-07
## pos_24_pd -1.532456e-05 -4.155083e-06
## pos_25_pd -1.378720e-05 -1.944884e-06
## pos_26_pd -1.331314e-05 -1.574143e-06
## pos_27_pd -1.533870e-05 -4.657655e-06
## pos_28_pd -1.329562e-05 -1.813360e-06
## pos_29_pd -1.727459e-05 -5.020296e-06
## pos_30_pd -1.221141e-05 4.239406e-07
## pos_31_pd -4.662830e-06 1.237751e-05
## pos_32_pd -1.280091e-05 1.022893e-05
## pos_33_pd -1.693527e-05 9.606784e-06
## pos_34_pd -1.845457e-05 1.713385e-05
## pos_35_pd -2.677365e-05 2.666542e-06
## pos_36_pd -2.342568e-05 -1.435736e-06
## pos_37_pd -1.467661e-05 1.587176e-05
## pos_38_pd -3.296841e-05 1.613912e-05
## pos_39_pd -4.235862e-05 2.397159e-05
## s(Time_Period_ID):as.factor(Region)Midwest.1 -2.640022e-05 -1.864013e-05
## s(Time_Period_ID):as.factor(Region)Midwest.2 -2.013501e-05 -1.437385e-05
## s(Time_Period_ID):as.factor(Region)Midwest.3 -8.399754e-06 -3.599267e-06
## s(Time_Period_ID):as.factor(Region)Midwest.4 -3.158193e-07 4.625205e-06
## s(Time_Period_ID):as.factor(Region)Midwest.5 7.163758e-06 1.142176e-05
## s(Time_Period_ID):as.factor(Region)Midwest.6 1.351382e-05 1.852194e-05
## s(Time_Period_ID):as.factor(Region)Midwest.7 2.268163e-05 2.938898e-05
## s(Time_Period_ID):as.factor(Region)Midwest.8 3.758518e-05 4.786244e-05
## s(Time_Period_ID):as.factor(Region)Midwest.9 2.922265e-05 4.221937e-05
## s(Time_Period_ID):as.factor(Region)Northeast.1 -3.376645e-05 -2.571216e-05
## s(Time_Period_ID):as.factor(Region)Northeast.2 -2.715192e-05 -2.068205e-05
## s(Time_Period_ID):as.factor(Region)Northeast.3 -7.775770e-06 -1.776697e-06
## s(Time_Period_ID):as.factor(Region)Northeast.4 -1.017321e-05 -4.355934e-06
## s(Time_Period_ID):as.factor(Region)Northeast.5 -9.497047e-06 -2.830569e-06
## s(Time_Period_ID):as.factor(Region)Northeast.6 1.544824e-06 8.662558e-06
## s(Time_Period_ID):as.factor(Region)Northeast.7 3.467209e-05 4.494980e-05
## s(Time_Period_ID):as.factor(Region)Northeast.8 7.938016e-05 9.100157e-05
## s(Time_Period_ID):as.factor(Region)Northeast.9 5.934945e-05 7.443454e-05
## s(Time_Period_ID):as.factor(Region)South.1 -2.824074e-05 -2.113765e-05
## s(Time_Period_ID):as.factor(Region)South.2 -1.601769e-05 -1.120885e-05
## s(Time_Period_ID):as.factor(Region)South.3 -1.728669e-06 3.964908e-06
## s(Time_Period_ID):as.factor(Region)South.4 4.351275e-06 1.007624e-05
## s(Time_Period_ID):as.factor(Region)South.5 1.354175e-05 1.860495e-05
## s(Time_Period_ID):as.factor(Region)South.6 1.637320e-05 2.195783e-05
## s(Time_Period_ID):as.factor(Region)South.7 2.859844e-05 3.560566e-05
## s(Time_Period_ID):as.factor(Region)South.8 5.024253e-05 6.216590e-05
## s(Time_Period_ID):as.factor(Region)South.9 3.351791e-05 5.259294e-05
## s(Time_Period_ID):as.factor(Region)West.1 -1.614422e-05 -1.176282e-05
## s(Time_Period_ID):as.factor(Region)West.2 -9.293793e-06 -5.525065e-06
## s(Time_Period_ID):as.factor(Region)West.3 -2.002912e-06 2.332601e-06
## s(Time_Period_ID):as.factor(Region)West.4 4.947686e-06 8.801392e-06
## s(Time_Period_ID):as.factor(Region)West.5 9.085742e-06 1.335974e-05
## s(Time_Period_ID):as.factor(Region)West.6 1.156459e-05 1.671415e-05
## s(Time_Period_ID):as.factor(Region)West.7 1.362680e-05 1.974457e-05
## s(Time_Period_ID):as.factor(Region)West.8 1.814801e-05 2.576047e-05
## s(Time_Period_ID):as.factor(Region)West.9 1.753132e-05 2.670057e-05
## ub_coef sd_coef
## (Intercept) 8.157547e-05 2.905074e-06
## StateAlaska 2.061533e-05 4.569480e-06
## StateArizona 2.395014e-05 3.163264e-06
## StateArkansas -1.775207e-05 3.501809e-06
## StateCalifornia -1.172615e-05 3.695578e-06
## StateColorado 6.929043e-06 3.648614e-06
## StateConnecticut 2.159818e-05 3.213467e-06
## StateDelaware 4.299841e-05 6.698533e-06
## StateFlorida 1.793385e-05 3.341016e-06
## StateGeorgia -5.179450e-06 3.685194e-06
## StateHawaii -1.915262e-05 3.690917e-06
## StateIdaho 5.248369e-06 3.170146e-06
## StateIllinois 8.699235e-06 3.110417e-06
## StateIndiana 2.002344e-05 2.915259e-06
## StateIowa -2.803673e-05 2.865495e-06
## StateKansas -1.140168e-05 2.390691e-06
## StateKentucky 6.802175e-05 3.404381e-06
## StateLouisiana 2.480617e-05 2.991510e-06
## StateMaine 1.826863e-05 3.878679e-06
## StateMaryland -4.747562e-05 3.869157e-06
## StateMassachusetts 2.860456e-05 3.503142e-06
## StateMichigan 8.021994e-06 2.619192e-06
## StateMinnesota -3.153424e-05 3.359916e-06
## StateMississippi 6.744176e-06 4.111735e-06
## StateMissouri 1.271329e-05 3.124578e-06
## StateMontana -2.698445e-05 3.096056e-06
## StateNebraska -2.816591e-05 3.151727e-06
## StateNevada 3.663927e-05 3.249801e-06
## StateNew Hampshire 2.594134e-05 3.863192e-06
## StateNew Jersey 1.054923e-05 3.622777e-06
## StateNew Mexico 5.863983e-05 3.773061e-06
## StateNew York 5.733091e-07 4.565213e-06
## StateNorth Carolina 1.548835e-05 2.353085e-06
## StateNorth Dakota -3.108441e-05 4.008816e-06
## StateOhio 5.238755e-05 7.188194e-06
## StateOklahoma 4.259911e-05 3.868445e-06
## StateOregon -1.591605e-05 3.335425e-06
## StatePennsylvania 4.855745e-05 3.478101e-06
## StateRhode Island 3.419899e-05 4.483319e-06
## StateSouth Carolina 2.464642e-05 3.179550e-06
## StateSouth Dakota -2.678978e-05 3.570635e-06
## StateTennessee 4.092187e-05 3.175156e-06
## StateTexas -1.314586e-07 4.121663e-06
## StateUtah 1.103432e-05 4.137463e-06
## StateVermont -3.100380e-06 4.428681e-06
## StateVirginia -5.841921e-07 2.660677e-06
## StateWashington 1.359632e-06 3.573279e-06
## StateWest Virginia 1.106453e-04 8.490531e-06
## StateWisconsin 2.008559e-06 2.987183e-06
## StateWyoming 7.666225e-06 3.043333e-06
## Naloxone_Pharmacy_Yes_Redefined 1.022656e-06 2.733609e-06
## Naloxone_Pharmacy_No_Redefined 2.559086e-06 2.125634e-06
## Medical_Marijuana_Redefined 1.553614e-05 2.342262e-06
## Recreational_Marijuana_Redefined -3.148625e-06 2.853901e-06
## GSL_Redefined 1.012160e-05 2.025831e-06
## PDMP_Redefined -1.283599e-05 1.586404e-06
## Medicaid_Expansion_Redefined 1.776483e-05 2.218035e-06
## neg_2_pd 5.035940e-06 2.796077e-06
## neg_3_pd 5.942481e-06 2.901611e-06
## neg_4_pd 2.891770e-06 3.057150e-06
## neg_5_pd -7.639754e-08 2.783792e-06
## neg_6_pd -5.235552e-07 2.708070e-06
## neg_7_pd -2.780750e-06 3.221525e-06
## neg_8_pd -3.948893e-06 4.032964e-06
## neg_9_pd -1.919866e-06 3.200330e-06
## neg_10_pd -2.423635e-06 2.982626e-06
## neg_11_pd -3.208452e-06 3.133367e-06
## neg_12_pd 1.263419e-06 3.681100e-06
## neg_13_pd -2.700889e-06 3.413465e-06
## neg_14_pd -2.843863e-06 3.994572e-06
## neg_15_pd -5.192220e-06 4.941209e-06
## neg_16_pd -7.091510e-06 3.773374e-06
## neg_17_pd -9.731808e-06 4.078431e-06
## neg_18_pd -1.042156e-05 4.207250e-06
## neg_19_pd -1.036893e-05 4.566398e-06
## neg_20_pd -1.257006e-05 4.636969e-06
## neg_21_pd -1.023457e-05 5.501905e-06
## neg_22_pd -7.627931e-06 6.955918e-06
## neg_23_pd -5.717382e-06 6.648554e-06
## neg_24_pd -7.904028e-06 7.703156e-06
## neg_25_pd -3.799090e-06 8.534948e-06
## neg_26_pd 2.921762e-06 9.808588e-06
## neg_27_pd -2.201551e-06 6.881178e-06
## neg_28_pd -2.757938e-06 6.285502e-06
## neg_29_pd -2.050340e-06 5.202754e-06
## neg_30_pd -5.524931e-06 5.803714e-06
## neg_31_pd -5.710045e-06 6.540777e-06
## neg_32_pd -4.568121e-06 7.248864e-06
## neg_33_pd 5.425142e-06 9.098279e-06
## pos_0_pd 5.629928e-06 2.859454e-06
## pos_1_pd 4.953275e-06 3.217279e-06
## pos_2_pd 7.935773e-06 3.209795e-06
## pos_3_pd 6.616271e-06 3.380412e-06
## pos_4_pd 7.504709e-06 3.536449e-06
## pos_5_pd 4.957829e-06 3.467055e-06
## pos_6_pd 8.213333e-06 4.070809e-06
## pos_7_pd 7.207585e-06 3.951273e-06
## pos_8_pd 6.810069e-06 4.428049e-06
## pos_9_pd 4.183794e-06 3.736887e-06
## pos_10_pd 4.070569e-06 3.808063e-06
## pos_11_pd 4.501821e-06 3.854539e-06
## pos_12_pd 5.147116e-06 3.646364e-06
## pos_13_pd 3.410312e-06 4.370594e-06
## pos_14_pd 4.407001e-06 4.120645e-06
## pos_15_pd 3.036962e-06 4.183160e-06
## pos_16_pd 2.488569e-06 4.410595e-06
## pos_17_pd 4.371486e-06 4.350578e-06
## pos_18_pd 5.013729e-06 4.340888e-06
## pos_19_pd 5.630775e-06 4.237579e-06
## pos_20_pd 4.801667e-06 4.464306e-06
## pos_21_pd 5.160940e-06 4.796747e-06
## pos_22_pd 8.004615e-06 4.994900e-06
## pos_23_pd 1.038017e-05 5.744830e-06
## pos_24_pd 7.014395e-06 5.698713e-06
## pos_25_pd 9.897435e-06 6.042000e-06
## pos_26_pd 1.016486e-05 5.989286e-06
## pos_27_pd 6.023389e-06 5.449512e-06
## pos_28_pd 9.668904e-06 5.858298e-06
## pos_29_pd 7.234001e-06 6.252192e-06
## pos_30_pd 1.305929e-05 6.446608e-06
## pos_31_pd 2.941786e-05 8.694053e-06
## pos_32_pd 3.325876e-05 1.174992e-05
## pos_33_pd 3.614884e-05 1.354187e-05
## pos_34_pd 5.272227e-05 1.815736e-05
## pos_35_pd 3.210673e-05 1.502051e-05
## pos_36_pd 2.055421e-05 1.121936e-05
## pos_37_pd 4.642012e-05 1.558590e-05
## pos_38_pd 6.524665e-05 2.505486e-05
## pos_39_pd 9.030181e-05 3.384195e-05
## s(Time_Period_ID):as.factor(Region)Midwest.1 -1.088004e-05 3.959229e-06
## s(Time_Period_ID):as.factor(Region)Midwest.2 -8.612697e-06 2.939365e-06
## s(Time_Period_ID):as.factor(Region)Midwest.3 1.201220e-06 2.449228e-06
## s(Time_Period_ID):as.factor(Region)Midwest.4 9.566229e-06 2.520931e-06
## s(Time_Period_ID):as.factor(Region)Midwest.5 1.567976e-05 2.172448e-06
## s(Time_Period_ID):as.factor(Region)Midwest.6 2.353006e-05 2.555163e-06
## s(Time_Period_ID):as.factor(Region)Midwest.7 3.609632e-05 3.422115e-06
## s(Time_Period_ID):as.factor(Region)Midwest.8 5.813971e-05 5.243501e-06
## s(Time_Period_ID):as.factor(Region)Midwest.9 5.521609e-05 6.630980e-06
## s(Time_Period_ID):as.factor(Region)Northeast.1 -1.765787e-05 4.109333e-06
## s(Time_Period_ID):as.factor(Region)Northeast.2 -1.421218e-05 3.300954e-06
## s(Time_Period_ID):as.factor(Region)Northeast.3 4.222376e-06 3.060752e-06
## s(Time_Period_ID):as.factor(Region)Northeast.4 1.461345e-06 2.968000e-06
## s(Time_Period_ID):as.factor(Region)Northeast.5 3.835908e-06 3.401264e-06
## s(Time_Period_ID):as.factor(Region)Northeast.6 1.578029e-05 3.631497e-06
## s(Time_Period_ID):as.factor(Region)Northeast.7 5.522750e-05 5.243728e-06
## s(Time_Period_ID):as.factor(Region)Northeast.8 1.026230e-04 5.929289e-06
## s(Time_Period_ID):as.factor(Region)Northeast.9 8.951963e-05 7.696475e-06
## s(Time_Period_ID):as.factor(Region)South.1 -1.403456e-05 3.624025e-06
## s(Time_Period_ID):as.factor(Region)South.2 -6.400009e-06 2.453490e-06
## s(Time_Period_ID):as.factor(Region)South.3 9.658485e-06 2.904886e-06
## s(Time_Period_ID):as.factor(Region)South.4 1.580121e-05 2.920901e-06
## s(Time_Period_ID):as.factor(Region)South.5 2.366816e-05 2.583268e-06
## s(Time_Period_ID):as.factor(Region)South.6 2.754245e-05 2.849298e-06
## s(Time_Period_ID):as.factor(Region)South.7 4.261288e-05 3.575113e-06
## s(Time_Period_ID):as.factor(Region)South.8 7.408928e-05 6.083354e-06
## s(Time_Period_ID):as.factor(Region)South.9 7.166797e-05 9.732157e-06
## s(Time_Period_ID):as.factor(Region)West.1 -7.381414e-06 2.235410e-06
## s(Time_Period_ID):as.factor(Region)West.2 -1.756337e-06 1.922820e-06
## s(Time_Period_ID):as.factor(Region)West.3 6.668115e-06 2.211997e-06
## s(Time_Period_ID):as.factor(Region)West.4 1.265510e-05 1.966176e-06
## s(Time_Period_ID):as.factor(Region)West.5 1.763374e-05 2.180611e-06
## s(Time_Period_ID):as.factor(Region)West.6 2.186371e-05 2.627328e-06
## s(Time_Period_ID):as.factor(Region)West.7 2.586233e-05 3.121310e-06
## s(Time_Period_ID):as.factor(Region)West.8 3.337294e-05 3.883911e-06
## s(Time_Period_ID):as.factor(Region)West.9 3.586982e-05 4.678189e-06
# write.csv(round(sensitivity_anlys_event_study_sd_and_ci, 3), "./Data/event_study_coef_and_ci.csv")
Plot Results
#plot the coefficients for the periods before and after the intervention with 95% CI
plot_event_study <- sensitivity_anlys_event_study_sd_and_ci %>%
mutate(term = rownames(sensitivity_anlys_event_study_sd_and_ci)) %>%
dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
filter(term %in% c(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2),
function(x){paste("neg_", x, "_pd", sep = "")}),
sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_event_study) <- c("term", "estimate", "conf.low", "conf.high")
dwplot(plot_event_study, colour = "black",
vars_order = c(sapply((max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0,
function(x){paste("pos_", x, "_pd", sep = "")}),
sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2),
function(x){paste("neg_", x, "_pd", sep = "")}))) +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black"),
axis.text.x = element_text(angle = 45)) +
geom_vline(aes(xintercept = 0), linetype = "dashed") +
labs(y = "States Excluded", x = "Coefficients and 95% Confidence Intervals",
title = "Coefficient of Pre-Intervention and Post-Intervention Periods") +
scale_color_grey() +
coord_flip() +
geom_hline(yintercept = 33, col = "red", linetype = "dashed")
Analysis With Only Periods After Treatment
formula_post_tx <- formula(paste("prop_dead~ State +
s(Time_Period_ID, bs = 'cr', by = as.factor(Region)) +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +",
paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_post_tx_model<-gam(formula_post_tx,
data = sensitivity_anlys_event_study_data)
summary(sensitivity_anlys_post_tx_model)
##
## Family: gaussian
## Link function: identity
##
## Formula:
## prop_dead ~ State + s(Time_Period_ID, bs = "cr", by = as.factor(Region)) +
## Naloxone_Pharmacy_Yes_Redefined + Naloxone_Pharmacy_No_Redefined +
## Medical_Marijuana_Redefined + Recreational_Marijuana_Redefined +
## GSL_Redefined + PDMP_Redefined + Medicaid_Expansion_Redefined +
## pos_0_pd + pos_1_pd + pos_2_pd + pos_3_pd + pos_4_pd + pos_5_pd +
## pos_6_pd + pos_7_pd + pos_8_pd + pos_9_pd + pos_10_pd + pos_11_pd +
## pos_12_pd + pos_13_pd + pos_14_pd + pos_15_pd + pos_16_pd +
## pos_17_pd + pos_18_pd + pos_19_pd + pos_20_pd + pos_21_pd +
## pos_22_pd + pos_23_pd + pos_24_pd + pos_25_pd + pos_26_pd +
## pos_27_pd + pos_28_pd + pos_29_pd + pos_30_pd + pos_31_pd +
## pos_32_pd + pos_33_pd + pos_34_pd + pos_35_pd + pos_36_pd +
## pos_37_pd + pos_38_pd + pos_39_pd
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.615e-05 3.494e-06 21.792 < 2e-16 ***
## StateAlaska -1.244e-07 4.815e-06 -0.026 0.979395
## StateArizona 1.048e-05 4.332e-06 2.419 0.015668 *
## StateArkansas -2.994e-05 4.258e-06 -7.032 2.84e-12 ***
## StateCalifornia -1.081e-05 4.866e-06 -2.222 0.026413 *
## StateColorado -6.902e-06 4.740e-06 -1.456 0.145555
## StateConnecticut 1.527e-05 4.502e-06 3.393 0.000707 ***
## StateDelaware 1.855e-05 4.405e-06 4.211 2.67e-05 ***
## StateFlorida 2.123e-05 4.454e-06 4.767 2.01e-06 ***
## StateGeorgia -1.127e-06 4.557e-06 -0.247 0.804631
## StateHawaii -2.801e-05 4.732e-06 -5.919 3.85e-09 ***
## StateIdaho -1.165e-05 4.300e-06 -2.709 0.006816 **
## StateIllinois 1.011e-05 4.410e-06 2.292 0.022016 *
## StateIndiana 1.100e-05 4.214e-06 2.610 0.009117 **
## StateIowa -2.866e-05 4.271e-06 -6.712 2.53e-11 ***
## StateKansas -1.528e-05 4.188e-06 -3.648 0.000272 ***
## StateKentucky 5.570e-05 4.257e-06 13.084 < 2e-16 ***
## StateLouisiana 2.460e-05 4.242e-06 5.799 7.82e-09 ***
## StateMaine 7.917e-06 4.699e-06 1.685 0.092192 .
## StateMaryland -4.704e-05 4.408e-06 -10.670 < 2e-16 ***
## StateMassachusetts 2.122e-05 4.267e-06 4.973 7.21e-07 ***
## StateMichigan 5.732e-06 4.363e-06 1.314 0.189042
## StateMinnesota -3.764e-05 4.434e-06 -8.487 < 2e-16 ***
## StateMississippi -1.064e-05 4.248e-06 -2.505 0.012340 *
## StateMissouri 1.052e-05 4.346e-06 2.420 0.015612 *
## StateMontana -2.781e-05 4.518e-06 -6.154 9.20e-10 ***
## StateNebraska -4.189e-05 4.300e-06 -9.743 < 2e-16 ***
## StateNevada 3.271e-05 4.577e-06 7.147 1.26e-12 ***
## StateNew Hampshire 1.527e-05 4.269e-06 3.578 0.000356 ***
## StateNew Jersey 1.124e-05 4.418e-06 2.544 0.011053 *
## StateNew Mexico 4.761e-05 4.644e-06 10.252 < 2e-16 ***
## StateNew York -7.913e-06 4.336e-06 -1.825 0.068146 .
## StateNorth Carolina 1.502e-05 4.204e-06 3.573 0.000362 ***
## StateNorth Dakota -4.662e-05 4.257e-06 -10.950 < 2e-16 ***
## StateOhio 4.935e-05 4.575e-06 10.786 < 2e-16 ***
## StateOklahoma 2.980e-05 4.230e-06 7.046 2.58e-12 ***
## StateOregon -2.570e-05 4.701e-06 -5.467 5.18e-08 ***
## StatePennsylvania 5.130e-05 4.467e-06 11.486 < 2e-16 ***
## StateRhode Island 1.597e-05 4.457e-06 3.582 0.000349 ***
## StateSouth Carolina 7.442e-06 4.287e-06 1.736 0.082689 .
## StateSouth Dakota -4.505e-05 4.326e-06 -10.413 < 2e-16 ***
## StateTennessee 3.460e-05 4.160e-06 8.317 < 2e-16 ***
## StateTexas 6.825e-07 4.430e-06 0.154 0.877569
## StateUtah 6.117e-06 4.212e-06 1.452 0.146556
## StateVermont -1.471e-05 4.429e-06 -3.321 0.000915 ***
## StateVirginia 4.207e-07 4.265e-06 0.099 0.921428
## StateWashington -7.392e-06 4.780e-06 -1.546 0.122161
## StateWest Virginia 8.612e-05 4.273e-06 20.157 < 2e-16 ***
## StateWisconsin 1.870e-06 4.251e-06 0.440 0.659998
## StateWyoming -8.478e-07 4.190e-06 -0.202 0.839667
## Naloxone_Pharmacy_Yes_Redefined -4.107e-06 2.766e-06 -1.485 0.137742
## Naloxone_Pharmacy_No_Redefined -1.422e-06 2.470e-06 -0.576 0.564837
## Medical_Marijuana_Redefined 1.175e-05 1.971e-06 5.962 2.96e-09 ***
## Recreational_Marijuana_Redefined -7.271e-06 3.118e-06 -2.332 0.019825 *
## GSL_Redefined 5.841e-06 2.019e-06 2.894 0.003853 **
## PDMP_Redefined -1.517e-05 1.577e-06 -9.625 < 2e-16 ***
## Medicaid_Expansion_Redefined 1.283e-05 1.946e-06 6.590 5.69e-11 ***
## pos_0_pd 1.590e-06 2.918e-06 0.545 0.585919
## pos_1_pd -4.270e-07 2.952e-06 -0.145 0.885022
## pos_2_pd 1.953e-06 2.987e-06 0.654 0.513330
## pos_3_pd -3.404e-07 3.025e-06 -0.113 0.910420
## pos_4_pd -4.024e-07 3.065e-06 -0.131 0.895557
## pos_5_pd -3.434e-06 3.114e-06 -1.103 0.270378
## pos_6_pd -1.994e-06 3.173e-06 -0.628 0.529849
## pos_7_pd -3.450e-06 3.228e-06 -1.069 0.285376
## pos_8_pd -5.473e-06 3.320e-06 -1.648 0.099438 .
## pos_9_pd -7.470e-06 3.394e-06 -2.201 0.027873 *
## pos_10_pd -8.429e-06 3.442e-06 -2.449 0.014421 *
## pos_11_pd -8.824e-06 3.518e-06 -2.508 0.012218 *
## pos_12_pd -8.503e-06 3.596e-06 -2.365 0.018153 *
## pos_13_pd -1.234e-05 3.651e-06 -3.380 0.000740 ***
## pos_14_pd -1.159e-05 3.785e-06 -3.062 0.002229 **
## pos_15_pd -1.383e-05 3.878e-06 -3.567 0.000371 ***
## pos_16_pd -1.553e-05 3.945e-06 -3.937 8.55e-05 ***
## pos_17_pd -1.427e-05 4.093e-06 -3.487 0.000499 ***
## pos_18_pd -1.435e-05 4.194e-06 -3.422 0.000635 ***
## pos_19_pd -1.417e-05 4.259e-06 -3.327 0.000896 ***
## pos_20_pd -1.620e-05 4.441e-06 -3.648 0.000271 ***
## pos_21_pd -1.719e-05 4.627e-06 -3.716 0.000208 ***
## pos_22_pd -1.544e-05 4.740e-06 -3.257 0.001145 **
## pos_23_pd -1.527e-05 4.877e-06 -3.130 0.001773 **
## pos_24_pd -1.916e-05 5.183e-06 -3.697 0.000225 ***
## pos_25_pd -1.759e-05 5.476e-06 -3.212 0.001338 **
## pos_26_pd -1.791e-05 5.535e-06 -3.236 0.001234 **
## pos_27_pd -2.179e-05 5.610e-06 -3.883 0.000107 ***
## pos_28_pd -1.954e-05 5.697e-06 -3.430 0.000617 ***
## pos_29_pd -2.341e-05 6.195e-06 -3.779 0.000162 ***
## pos_30_pd -1.866e-05 6.400e-06 -2.916 0.003586 **
## pos_31_pd -7.543e-06 6.621e-06 -1.139 0.254670
## pos_32_pd -1.054e-05 7.294e-06 -1.445 0.148697
## pos_33_pd -1.192e-05 7.629e-06 -1.562 0.118365
## pos_34_pd -5.050e-06 7.709e-06 -0.655 0.512508
## pos_35_pd -2.019e-05 8.956e-06 -2.254 0.024301 *
## pos_36_pd -2.494e-05 9.045e-06 -2.758 0.005875 **
## pos_37_pd -8.400e-06 1.070e-05 -0.785 0.432654
## pos_38_pd -8.735e-06 1.429e-05 -0.611 0.541172
## pos_39_pd -1.579e-06 1.446e-05 -0.109 0.913036
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(Time_Period_ID):as.factor(Region)Midwest 6.822 7.911 49.06 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)Northeast 8.047 8.756 79.14 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)South 7.779 8.613 73.93 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)West 3.300 4.122 62.06 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.835 Deviance explained = 84.5%
## GCV = 3.6751e-10 Scale est. = 3.4492e-10 n = 2000
Sandwich Estimator
#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_post_tx <- data.frame(predict(sensitivity_anlys_post_tx_model, type = "lpmatrix"))
#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_post_tx <- coef(sensitivity_anlys_post_tx_model)
sensitivity_anlys_post_tx_sd_and_ci <- compute_sd_and_CI(as.matrix(full_df_w_basis_functions_sensitivity_anlys_post_tx),
sensitivity_anlys_event_study_data$prop_dead,
coefficient_values_sensitivity_anlys_post_tx,
p = ncol(full_df_w_basis_functions_sensitivity_anlys_post_tx) - 50)
sensitivity_anlys_post_tx_sd_and_ci
## lb_coef coef_values
## (Intercept) 7.139855e-05 7.615063e-05
## StateAlaska -8.051122e-06 -1.243671e-07
## StateArizona 4.830838e-06 1.047917e-05
## StateArkansas -3.660598e-05 -2.994465e-05
## StateCalifornia -1.778510e-05 -1.081069e-05
## StateColorado -1.359417e-05 -6.902221e-06
## StateConnecticut 9.002599e-06 1.527196e-05
## StateDelaware 6.704041e-06 1.854851e-05
## StateFlorida 1.543359e-05 2.123426e-05
## StateGeorgia -7.525247e-06 -1.127323e-06
## StateHawaii -3.507774e-05 -2.800827e-05
## StateIdaho -1.651843e-05 -1.164810e-05
## StateIllinois 4.319206e-06 1.010830e-05
## StateIndiana 5.286176e-06 1.099931e-05
## StateIowa -3.385601e-05 -2.866399e-05
## StateKansas -1.986427e-05 -1.527660e-05
## StateKentucky 4.906042e-05 5.569746e-05
## StateLouisiana 1.912834e-05 2.459979e-05
## StateMaine 4.714770e-07 7.917008e-06
## StateMaryland -5.429863e-05 -4.703545e-05
## StateMassachusetts 1.436466e-05 2.121827e-05
## StateMichigan 6.996377e-07 5.732447e-06
## StateMinnesota -4.409755e-05 -3.763627e-05
## StateMississippi -1.787561e-05 -1.063882e-05
## StateMissouri 4.692188e-06 1.051648e-05
## StateMontana -3.355921e-05 -2.780680e-05
## StateNebraska -4.762309e-05 -4.188786e-05
## StateNevada 2.640169e-05 3.271259e-05
## StateNew Hampshire 7.772563e-06 1.527174e-05
## StateNew Jersey 4.575249e-06 1.123726e-05
## StateNew Mexico 4.036531e-05 4.761186e-05
## StateNew York -1.675067e-05 -7.913039e-06
## StateNorth Carolina 1.067636e-05 1.501899e-05
## StateNorth Dakota -5.398294e-05 -4.661541e-05
## StateOhio 3.566787e-05 4.935159e-05
## StateOklahoma 2.243402e-05 2.980233e-05
## StateOregon -3.202076e-05 -2.570197e-05
## StatePennsylvania 4.492220e-05 5.130490e-05
## StateRhode Island 7.594812e-06 1.596700e-05
## StateSouth Carolina 2.721784e-06 7.442319e-06
## StateSouth Dakota -5.143228e-05 -4.504805e-05
## StateTennessee 2.848882e-05 3.459578e-05
## StateTexas -7.215531e-06 6.825124e-07
## StateUtah -2.039631e-06 6.116769e-06
## StateVermont -2.327214e-05 -1.470731e-05
## StateVirginia -4.587674e-06 4.206861e-07
## StateWashington -1.429859e-05 -7.391705e-06
## StateWest Virginia 6.951595e-05 8.612320e-05
## StateWisconsin -3.533923e-06 1.870202e-06
## StateWyoming -6.889956e-06 -8.478496e-07
## Naloxone_Pharmacy_Yes_Redefined -9.432775e-06 -4.107253e-06
## Naloxone_Pharmacy_No_Redefined -5.568562e-06 -1.422226e-06
## Medical_Marijuana_Redefined 7.199413e-06 1.175190e-05
## Recreational_Marijuana_Redefined -1.262468e-05 -7.270518e-06
## GSL_Redefined 1.904319e-06 5.840877e-06
## PDMP_Redefined -1.822667e-05 -1.517500e-05
## Medicaid_Expansion_Redefined 8.537038e-06 1.282744e-05
## pos_0_pd -2.965098e-06 1.589816e-06
## pos_1_pd -5.840947e-06 -4.269689e-07
## pos_2_pd -3.408478e-06 1.952849e-06
## pos_3_pd -6.011940e-06 -3.403996e-07
## pos_4_pd -6.289188e-06 -4.023682e-07
## pos_5_pd -9.197525e-06 -3.433682e-06
## pos_6_pd -8.932879e-06 -1.993884e-06
## pos_7_pd -1.022580e-05 -3.449720e-06
## pos_8_pd -1.313667e-05 -5.473039e-06
## pos_9_pd -1.385605e-05 -7.469612e-06
## pos_10_pd -1.500229e-05 -8.429489e-06
## pos_11_pd -1.540069e-05 -8.823831e-06
## pos_12_pd -1.471607e-05 -8.502757e-06
## pos_13_pd -1.999956e-05 -1.233928e-05
## pos_14_pd -1.858506e-05 -1.158885e-05
## pos_15_pd -2.092374e-05 -1.383004e-05
## pos_16_pd -2.312394e-05 -1.553093e-05
## pos_17_pd -2.177377e-05 -1.427438e-05
## pos_18_pd -2.158529e-05 -1.435308e-05
## pos_19_pd -2.127088e-05 -1.416703e-05
## pos_20_pd -2.355906e-05 -1.620249e-05
## pos_21_pd -2.521230e-05 -1.719404e-05
## pos_22_pd -2.388111e-05 -1.544116e-05
## pos_23_pd -2.529719e-05 -1.526768e-05
## pos_24_pd -2.909569e-05 -1.916142e-05
## pos_25_pd -2.826441e-05 -1.759028e-05
## pos_26_pd -2.860727e-05 -1.791097e-05
## pos_27_pd -3.099788e-05 -2.178720e-05
## pos_28_pd -2.973838e-05 -1.953942e-05
## pos_29_pd -3.442329e-05 -2.341014e-05
## pos_30_pd -3.009266e-05 -1.866474e-05
## pos_31_pd -2.356847e-05 -7.543544e-06
## pos_32_pd -3.271810e-05 -1.053846e-05
## pos_33_pd -3.773946e-05 -1.191918e-05
## pos_34_pd -4.012237e-05 -5.049810e-06
## pos_35_pd -4.883116e-05 -2.018769e-05
## pos_36_pd -4.583816e-05 -2.494403e-05
## pos_37_pd -3.797048e-05 -8.400120e-06
## pos_38_pd -5.707690e-05 -8.735278e-06
## pos_39_pd -6.713461e-05 -1.579383e-06
## s(Time_Period_ID):as.factor(Region)Midwest.1 -3.211010e-05 -2.493444e-05
## s(Time_Period_ID):as.factor(Region)Midwest.2 -2.371188e-05 -1.830146e-05
## s(Time_Period_ID):as.factor(Region)Midwest.3 -9.157463e-06 -4.474457e-06
## s(Time_Period_ID):as.factor(Region)Midwest.4 1.423613e-06 6.323655e-06
## s(Time_Period_ID):as.factor(Region)Midwest.5 1.213292e-05 1.641477e-05
## s(Time_Period_ID):as.factor(Region)Midwest.6 2.158643e-05 2.650577e-05
## s(Time_Period_ID):as.factor(Region)Midwest.7 3.422336e-05 4.037425e-05
## s(Time_Period_ID):as.factor(Region)Midwest.8 5.252596e-05 6.239041e-05
## s(Time_Period_ID):as.factor(Region)Midwest.9 4.466238e-05 5.730285e-05
## s(Time_Period_ID):as.factor(Region)Northeast.1 -3.872057e-05 -3.093339e-05
## s(Time_Period_ID):as.factor(Region)Northeast.2 -3.149449e-05 -2.507869e-05
## s(Time_Period_ID):as.factor(Region)Northeast.3 -7.592004e-06 -1.599376e-06
## s(Time_Period_ID):as.factor(Region)Northeast.4 -6.658618e-06 -1.012325e-06
## s(Time_Period_ID):as.factor(Region)Northeast.5 -3.754892e-06 2.525880e-06
## s(Time_Period_ID):as.factor(Region)Northeast.6 1.069200e-05 1.736867e-05
## s(Time_Period_ID):as.factor(Region)Northeast.7 4.670155e-05 5.626171e-05
## s(Time_Period_ID):as.factor(Region)Northeast.8 9.516824e-05 1.060037e-04
## s(Time_Period_ID):as.factor(Region)Northeast.9 7.494540e-05 8.947043e-05
## s(Time_Period_ID):as.factor(Region)South.1 -3.385393e-05 -2.733642e-05
## s(Time_Period_ID):as.factor(Region)South.2 -2.045537e-05 -1.584398e-05
## s(Time_Period_ID):as.factor(Region)South.3 -3.048268e-06 2.516412e-06
## s(Time_Period_ID):as.factor(Region)South.4 6.282816e-06 1.198599e-05
## s(Time_Period_ID):as.factor(Region)South.5 1.908371e-05 2.394614e-05
## s(Time_Period_ID):as.factor(Region)South.6 2.476099e-05 2.985264e-05
## s(Time_Period_ID):as.factor(Region)South.7 4.033239e-05 4.676438e-05
## s(Time_Period_ID):as.factor(Region)South.8 6.465526e-05 7.656179e-05
## s(Time_Period_ID):as.factor(Region)South.9 4.922028e-05 6.782284e-05
## s(Time_Period_ID):as.factor(Region)West.1 -2.196381e-05 -1.743681e-05
## s(Time_Period_ID):as.factor(Region)West.2 -1.269009e-05 -9.040207e-06
## s(Time_Period_ID):as.factor(Region)West.3 -2.486098e-06 1.767265e-06
## s(Time_Period_ID):as.factor(Region)West.4 7.415034e-06 1.114857e-05
## s(Time_Period_ID):as.factor(Region)West.5 1.461424e-05 1.850163e-05
## s(Time_Period_ID):as.factor(Region)West.6 1.993230e-05 2.454423e-05
## s(Time_Period_ID):as.factor(Region)West.7 2.454761e-05 3.005842e-05
## s(Time_Period_ID):as.factor(Region)West.8 3.212598e-05 3.927979e-05
## s(Time_Period_ID):as.factor(Region)West.9 3.218580e-05 4.072767e-05
## ub_coef sd_coef
## (Intercept) 8.090271e-05 2.424530e-06
## StateAlaska 7.802388e-06 4.044263e-06
## StateArizona 1.612749e-05 2.881800e-06
## StateArkansas -2.328331e-05 3.398640e-06
## StateCalifornia -3.836271e-06 3.558376e-06
## StateColorado -2.102737e-07 3.414259e-06
## StateConnecticut 2.154131e-05 3.198651e-06
## StateDelaware 3.039297e-05 6.043094e-06
## StateFlorida 2.703492e-05 2.959524e-06
## StateGeorgia 5.270602e-06 3.264247e-06
## StateHawaii -2.093881e-05 3.606869e-06
## StateIdaho -6.777775e-06 2.484862e-06
## StateIllinois 1.589740e-05 2.953622e-06
## StateIndiana 1.671244e-05 2.914864e-06
## StateIowa -2.347198e-05 2.648987e-06
## StateKansas -1.068894e-05 2.340648e-06
## StateKentucky 6.233450e-05 3.386243e-06
## StateLouisiana 3.007123e-05 2.791554e-06
## StateMaine 1.536254e-05 3.798740e-06
## StateMaryland -3.977228e-05 3.705704e-06
## StateMassachusetts 2.807187e-05 3.496738e-06
## StateMichigan 1.076526e-05 2.567760e-06
## StateMinnesota -3.117500e-05 3.296567e-06
## StateMississippi -3.402037e-06 3.692238e-06
## StateMissouri 1.634077e-05 2.971578e-06
## StateMontana -2.205439e-05 2.934903e-06
## StateNebraska -3.615263e-05 2.926138e-06
## StateNevada 3.902349e-05 3.219848e-06
## StateNew Hampshire 2.277091e-05 3.826109e-06
## StateNew Jersey 1.789928e-05 3.398987e-06
## StateNew Mexico 5.485840e-05 3.697216e-06
## StateNew York 9.245956e-07 4.508997e-06
## StateNorth Carolina 1.936162e-05 2.215627e-06
## StateNorth Dakota -3.924788e-05 3.758944e-06
## StateOhio 6.303530e-05 6.981486e-06
## StateOklahoma 3.717064e-05 3.759342e-06
## StateOregon -1.938317e-05 3.223875e-06
## StatePennsylvania 5.768761e-05 3.256481e-06
## StateRhode Island 2.433920e-05 4.271527e-06
## StateSouth Carolina 1.216285e-05 2.408436e-06
## StateSouth Dakota -3.866382e-05 3.257261e-06
## StateTennessee 4.070274e-05 3.115794e-06
## StateTexas 8.580556e-06 4.029614e-06
## StateUtah 1.427317e-05 4.161429e-06
## StateVermont -6.142477e-06 4.369811e-06
## StateVirginia 5.429046e-06 2.555286e-06
## StateWashington -4.848192e-07 3.523921e-06
## StateWest Virginia 1.027305e-04 8.473088e-06
## StateWisconsin 7.274327e-06 2.757207e-06
## StateWyoming 5.194256e-06 3.082707e-06
## Naloxone_Pharmacy_Yes_Redefined 1.218270e-06 2.717103e-06
## Naloxone_Pharmacy_No_Redefined 2.724111e-06 2.115478e-06
## Medical_Marijuana_Redefined 1.630438e-05 2.322695e-06
## Recreational_Marijuana_Redefined -1.916352e-06 2.731717e-06
## GSL_Redefined 9.777435e-06 2.008448e-06
## PDMP_Redefined -1.212333e-05 1.556976e-06
## Medicaid_Expansion_Redefined 1.711783e-05 2.188979e-06
## pos_0_pd 6.144729e-06 2.323936e-06
## pos_1_pd 4.987009e-06 2.762233e-06
## pos_2_pd 7.314176e-06 2.735371e-06
## pos_3_pd 5.331141e-06 2.893643e-06
## pos_4_pd 5.484452e-06 3.003480e-06
## pos_5_pd 2.330162e-06 2.940736e-06
## pos_6_pd 4.945110e-06 3.540303e-06
## pos_7_pd 3.326362e-06 3.457185e-06
## pos_8_pd 2.190595e-06 3.910018e-06
## pos_9_pd -1.083178e-06 3.258385e-06
## pos_10_pd -1.856691e-06 3.353469e-06
## pos_11_pd -2.246967e-06 3.355543e-06
## pos_12_pd -2.289445e-06 3.170057e-06
## pos_13_pd -4.678991e-06 3.908308e-06
## pos_14_pd -4.592634e-06 3.569496e-06
## pos_15_pd -6.736345e-06 3.619233e-06
## pos_16_pd -7.937906e-06 3.873990e-06
## pos_17_pd -6.774981e-06 3.826223e-06
## pos_18_pd -7.120875e-06 3.689901e-06
## pos_19_pd -7.063178e-06 3.624413e-06
## pos_20_pd -8.845924e-06 3.753351e-06
## pos_21_pd -9.175768e-06 4.090953e-06
## pos_22_pd -7.001196e-06 4.306102e-06
## pos_23_pd -5.238178e-06 5.117094e-06
## pos_24_pd -9.227145e-06 5.068507e-06
## pos_25_pd -6.916147e-06 5.445985e-06
## pos_26_pd -7.214666e-06 5.457296e-06
## pos_27_pd -1.257652e-05 4.699326e-06
## pos_28_pd -9.340455e-06 5.203553e-06
## pos_29_pd -1.239698e-05 5.618957e-06
## pos_30_pd -7.236820e-06 5.830571e-06
## pos_31_pd 8.481383e-06 8.175983e-06
## pos_32_pd 1.164118e-05 1.131614e-05
## pos_33_pd 1.390111e-05 1.317361e-05
## pos_34_pd 3.002275e-05 1.789416e-05
## pos_35_pd 8.455787e-06 1.461402e-05
## pos_36_pd -4.049895e-06 1.066027e-05
## pos_37_pd 2.117024e-05 1.508692e-05
## pos_38_pd 3.960634e-05 2.466409e-05
## pos_39_pd 6.397585e-05 3.344655e-05
## s(Time_Period_ID):as.factor(Region)Midwest.1 -1.775878e-05 3.661052e-06
## s(Time_Period_ID):as.factor(Region)Midwest.2 -1.289103e-05 2.760421e-06
## s(Time_Period_ID):as.factor(Region)Midwest.3 2.085494e-07 2.389289e-06
## s(Time_Period_ID):as.factor(Region)Midwest.4 1.122370e-05 2.500022e-06
## s(Time_Period_ID):as.factor(Region)Midwest.5 2.069662e-05 2.184618e-06
## s(Time_Period_ID):as.factor(Region)Midwest.6 3.142512e-05 2.509869e-06
## s(Time_Period_ID):as.factor(Region)Midwest.7 4.652513e-05 3.138207e-06
## s(Time_Period_ID):as.factor(Region)Midwest.8 7.225486e-05 5.032883e-06
## s(Time_Period_ID):as.factor(Region)Midwest.9 6.994333e-05 6.449222e-06
## s(Time_Period_ID):as.factor(Region)Northeast.1 -2.314621e-05 3.973050e-06
## s(Time_Period_ID):as.factor(Region)Northeast.2 -1.866289e-05 3.273368e-06
## s(Time_Period_ID):as.factor(Region)Northeast.3 4.393252e-06 3.057463e-06
## s(Time_Period_ID):as.factor(Region)Northeast.4 4.633969e-06 2.880762e-06
## s(Time_Period_ID):as.factor(Region)Northeast.5 8.806652e-06 3.204475e-06
## s(Time_Period_ID):as.factor(Region)Northeast.6 2.404534e-05 3.406465e-06
## s(Time_Period_ID):as.factor(Region)Northeast.7 6.582187e-05 4.877632e-06
## s(Time_Period_ID):as.factor(Region)Northeast.8 1.168392e-04 5.528309e-06
## s(Time_Period_ID):as.factor(Region)Northeast.9 1.039955e-04 7.410729e-06
## s(Time_Period_ID):as.factor(Region)South.1 -2.081890e-05 3.325264e-06
## s(Time_Period_ID):as.factor(Region)South.2 -1.123259e-05 2.352751e-06
## s(Time_Period_ID):as.factor(Region)South.3 8.081093e-06 2.839123e-06
## s(Time_Period_ID):as.factor(Region)South.4 1.768916e-05 2.909781e-06
## s(Time_Period_ID):as.factor(Region)South.5 2.880856e-05 2.480828e-06
## s(Time_Period_ID):as.factor(Region)South.6 3.494430e-05 2.597782e-06
## s(Time_Period_ID):as.factor(Region)South.7 5.319637e-05 3.281626e-06
## s(Time_Period_ID):as.factor(Region)South.8 8.846831e-05 6.074756e-06
## s(Time_Period_ID):as.factor(Region)South.9 8.642540e-05 9.491102e-06
## s(Time_Period_ID):as.factor(Region)West.1 -1.290981e-05 2.309694e-06
## s(Time_Period_ID):as.factor(Region)West.2 -5.390325e-06 1.862185e-06
## s(Time_Period_ID):as.factor(Region)West.3 6.020627e-06 2.170083e-06
## s(Time_Period_ID):as.factor(Region)West.4 1.488210e-05 1.904864e-06
## s(Time_Period_ID):as.factor(Region)West.5 2.238901e-05 1.983359e-06
## s(Time_Period_ID):as.factor(Region)West.6 2.915617e-05 2.353027e-06
## s(Time_Period_ID):as.factor(Region)West.7 3.556922e-05 2.811635e-06
## s(Time_Period_ID):as.factor(Region)West.8 4.643359e-05 3.649901e-06
## s(Time_Period_ID):as.factor(Region)West.9 4.926954e-05 4.358096e-06
Plot Results
#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx <- sensitivity_anlys_post_tx_sd_and_ci %>%
mutate(term = rownames(sensitivity_anlys_post_tx_sd_and_ci)) %>%
dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
filter(term %in% c(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_post_tx) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx$num_states <- sapply(plot_post_tx$term, function(x){sum(sensitivity_anlys_event_study_data[,x])})
dwplot(plot_post_tx, colour = "black",
vars_order = c(sapply(((max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0),
function(x){paste("pos_", x, "_pd", sep = "")}))) +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black"),
axis.text.x = element_text(angle = 45, size = 4)) +
geom_vline(aes(xintercept = 0), linetype = "dashed") +
labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals",
title = "Coefficient of Pre-Intervention and Post-Intervention Periods") +
scale_color_grey() +
coord_flip() +
geom_vline(aes(xintercept = coef(main_analysis_model)["Intervention_Redefined"]), linetype = "dashed", color = "red") +
geom_text(aes(label = paste("Coefficient Estimate: ", coef(main_analysis_model)["Intervention_Redefined"]), y = 12,
x = coef(main_analysis_model)["Intervention_Redefined"] + 0.00001), color = "red")
# geom_text(aes(label = num_states, x = .1, y = 40:1), size = 2)
OLS Model Main Analysis With Fixed Time Effects
#compute the proportion of people who died from drug overdose
main_analysis_data$prop_dead <- main_analysis_data$imputed_deaths/main_analysis_data$population
#fit an OLS with smoothed time effects
main_analysis_model_fixed_time<-lm(prop_dead~ State +
factor(Time_Period_ID) +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +
Intervention_Redefined ,
data = main_analysis_data)
summary(main_analysis_model_fixed_time)
##
## Call:
## lm(formula = prop_dead ~ State + factor(Time_Period_ID) + Naloxone_Pharmacy_Yes_Redefined +
## Naloxone_Pharmacy_No_Redefined + Medical_Marijuana_Redefined +
## Recreational_Marijuana_Redefined + GSL_Redefined + PDMP_Redefined +
## Medicaid_Expansion_Redefined + Intervention_Redefined, data = main_analysis_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.033e-04 -1.127e-05 2.730e-07 1.060e-05 1.329e-04
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.690e-05 4.477e-06 6.008 2.25e-09 ***
## StateAlaska -4.545e-07 5.233e-06 -0.087 0.930802
## StateArizona 1.056e-05 4.810e-06 2.196 0.028199 *
## StateArkansas -2.812e-05 4.749e-06 -5.922 3.77e-09 ***
## StateCalifornia -2.297e-05 5.226e-06 -4.395 1.17e-05 ***
## StateColorado -7.966e-06 5.206e-06 -1.530 0.126127
## StateConnecticut 1.233e-05 5.019e-06 2.457 0.014117 *
## StateDelaware 2.026e-05 4.829e-06 4.196 2.84e-05 ***
## StateFlorida 1.477e-05 4.752e-06 3.107 0.001916 **
## StateGeorgia -6.738e-06 4.753e-06 -1.418 0.156481
## StateHawaii -3.119e-05 5.155e-06 -6.050 1.74e-09 ***
## StateIdaho -7.178e-06 4.753e-06 -1.510 0.131165
## StateIllinois 2.423e-06 4.821e-06 0.503 0.615249
## StateIndiana 1.231e-05 4.727e-06 2.605 0.009264 **
## StateIowa -3.167e-05 4.738e-06 -6.684 3.04e-11 ***
## StateKansas -1.520e-05 4.703e-06 -3.231 0.001256 **
## StateKentucky 5.787e-05 4.759e-06 12.160 < 2e-16 ***
## StateLouisiana 2.101e-05 4.698e-06 4.472 8.20e-06 ***
## StateMaine 2.151e-06 5.217e-06 0.412 0.680224
## StateMaryland -5.345e-05 4.810e-06 -11.111 < 2e-16 ***
## StateMassachusetts 1.973e-05 4.784e-06 4.125 3.87e-05 ***
## StateMichigan -5.122e-07 4.853e-06 -0.106 0.915949
## StateMinnesota -4.436e-05 4.934e-06 -8.992 < 2e-16 ***
## StateMississippi -6.311e-06 4.701e-06 -1.342 0.179598
## StateMissouri 8.772e-06 4.858e-06 1.806 0.071105 .
## StateMontana -3.690e-05 4.968e-06 -7.428 1.66e-13 ***
## StateNebraska -3.727e-05 4.777e-06 -7.803 9.88e-15 ***
## StateNevada 2.442e-05 5.062e-06 4.823 1.53e-06 ***
## StateNew Hampshire 1.473e-05 4.771e-06 3.087 0.002050 **
## StateNew Jersey 3.229e-06 4.816e-06 0.671 0.502590
## StateNew Mexico 4.375e-05 5.128e-06 8.530 < 2e-16 ***
## StateNew York -1.106e-05 4.854e-06 -2.279 0.022773 *
## StateNorth Carolina 1.177e-05 4.689e-06 2.509 0.012188 *
## StateNorth Dakota -4.407e-05 4.731e-06 -9.315 < 2e-16 ***
## StateOhio 4.235e-05 4.764e-06 8.891 < 2e-16 ***
## StateOklahoma 3.111e-05 4.732e-06 6.575 6.27e-11 ***
## StateOregon -3.003e-05 5.188e-06 -5.788 8.33e-09 ***
## StatePennsylvania 4.396e-05 4.757e-06 9.240 < 2e-16 ***
## StateRhode Island 1.390e-05 4.914e-06 2.829 0.004725 **
## StateSouth Carolina 1.253e-05 4.727e-06 2.651 0.008097 **
## StateSouth Dakota -3.960e-05 4.754e-06 -8.329 < 2e-16 ***
## StateTennessee 3.433e-05 4.677e-06 7.340 3.15e-13 ***
## StateTexas -4.871e-06 4.751e-06 -1.025 0.305395
## StateUtah 3.050e-06 4.705e-06 0.648 0.516817
## StateVermont -1.916e-05 4.922e-06 -3.892 0.000103 ***
## StateVirginia -3.600e-06 4.698e-06 -0.766 0.443607
## StateWashington -1.092e-05 5.268e-06 -2.073 0.038334 *
## StateWest Virginia 8.857e-05 4.757e-06 18.617 < 2e-16 ***
## StateWisconsin -1.369e-06 4.708e-06 -0.291 0.771148
## StateWyoming 5.620e-07 4.702e-06 0.120 0.904871
## factor(Time_Period_ID)2 -9.184e-07 4.177e-06 -0.220 0.826005
## factor(Time_Period_ID)3 1.447e-06 4.179e-06 0.346 0.729219
## factor(Time_Period_ID)4 3.163e-06 4.181e-06 0.756 0.449452
## factor(Time_Period_ID)5 8.631e-06 4.183e-06 2.064 0.039193 *
## factor(Time_Period_ID)6 9.444e-06 4.187e-06 2.255 0.024226 *
## factor(Time_Period_ID)7 1.471e-05 4.189e-06 3.512 0.000455 ***
## factor(Time_Period_ID)8 1.452e-05 4.192e-06 3.465 0.000543 ***
## factor(Time_Period_ID)9 1.750e-05 4.198e-06 4.168 3.21e-05 ***
## factor(Time_Period_ID)10 1.699e-05 4.208e-06 4.036 5.65e-05 ***
## factor(Time_Period_ID)11 2.134e-05 4.217e-06 5.061 4.56e-07 ***
## factor(Time_Period_ID)12 2.224e-05 4.238e-06 5.247 1.72e-07 ***
## factor(Time_Period_ID)13 3.016e-05 4.251e-06 7.094 1.83e-12 ***
## factor(Time_Period_ID)14 3.341e-05 4.269e-06 7.827 8.23e-15 ***
## factor(Time_Period_ID)15 3.514e-05 4.269e-06 8.230 3.43e-16 ***
## factor(Time_Period_ID)16 3.590e-05 4.288e-06 8.373 < 2e-16 ***
## factor(Time_Period_ID)17 4.012e-05 4.325e-06 9.277 < 2e-16 ***
## factor(Time_Period_ID)18 3.897e-05 4.345e-06 8.969 < 2e-16 ***
## factor(Time_Period_ID)19 3.949e-05 4.361e-06 9.055 < 2e-16 ***
## factor(Time_Period_ID)20 3.882e-05 4.388e-06 8.848 < 2e-16 ***
## factor(Time_Period_ID)21 4.242e-05 4.411e-06 9.617 < 2e-16 ***
## factor(Time_Period_ID)22 4.040e-05 4.443e-06 9.092 < 2e-16 ***
## factor(Time_Period_ID)23 4.922e-05 4.461e-06 11.034 < 2e-16 ***
## factor(Time_Period_ID)24 4.817e-05 4.511e-06 10.679 < 2e-16 ***
## factor(Time_Period_ID)25 4.778e-05 4.527e-06 10.555 < 2e-16 ***
## factor(Time_Period_ID)26 4.763e-05 4.552e-06 10.463 < 2e-16 ***
## factor(Time_Period_ID)27 5.359e-05 4.597e-06 11.657 < 2e-16 ***
## factor(Time_Period_ID)28 5.148e-05 4.644e-06 11.086 < 2e-16 ***
## factor(Time_Period_ID)29 5.252e-05 4.703e-06 11.169 < 2e-16 ***
## factor(Time_Period_ID)30 5.345e-05 4.787e-06 11.166 < 2e-16 ***
## factor(Time_Period_ID)31 6.133e-05 4.834e-06 12.686 < 2e-16 ***
## factor(Time_Period_ID)32 6.292e-05 5.050e-06 12.460 < 2e-16 ***
## factor(Time_Period_ID)33 7.678e-05 5.153e-06 14.900 < 2e-16 ***
## factor(Time_Period_ID)34 8.123e-05 5.361e-06 15.153 < 2e-16 ***
## factor(Time_Period_ID)35 8.909e-05 5.424e-06 16.426 < 2e-16 ***
## factor(Time_Period_ID)36 8.729e-05 5.524e-06 15.801 < 2e-16 ***
## factor(Time_Period_ID)37 8.433e-05 5.528e-06 15.254 < 2e-16 ***
## factor(Time_Period_ID)38 8.291e-05 5.553e-06 14.931 < 2e-16 ***
## factor(Time_Period_ID)39 8.255e-05 5.570e-06 14.822 < 2e-16 ***
## factor(Time_Period_ID)40 9.261e-05 5.576e-06 16.608 < 2e-16 ***
## Naloxone_Pharmacy_Yes_Redefined -1.490e-06 3.098e-06 -0.481 0.630612
## Naloxone_Pharmacy_No_Redefined -1.381e-06 2.633e-06 -0.525 0.599951
## Medical_Marijuana_Redefined 2.002e-05 2.074e-06 9.654 < 2e-16 ***
## Recreational_Marijuana_Redefined -1.896e-05 3.136e-06 -6.047 1.77e-09 ***
## GSL_Redefined 6.260e-06 2.199e-06 2.847 0.004464 **
## PDMP_Redefined -1.397e-05 1.744e-06 -8.009 2.00e-15 ***
## Medicaid_Expansion_Redefined 1.238e-05 2.148e-06 5.761 9.75e-09 ***
## Intervention_Redefined -3.057e-07 1.705e-06 -0.179 0.857773
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.088e-05 on 1903 degrees of freedom
## Multiple R-squared: 0.8009, Adjusted R-squared: 0.7908
## F-statistic: 79.72 on 96 and 1903 DF, p-value: < 2.2e-16
#examine fitted values
summary(fitted(main_analysis_model_fixed_time))
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.746e-05 4.210e-05 6.466e-05 6.974e-05 9.474e-05 2.310e-04
hist(fitted(main_analysis_model_fixed_time))
par(mfrow = c(2,2))
plot(main_analysis_model_fixed_time)
Coefficients and 95% CI
#compute the full dataset including basis functions
full_df_w_basis_functions_fixed_time <- model.matrix(main_analysis_model_fixed_time)
#estimate the 95% CI and SD
coefficient_values_fixed_time <- coef(main_analysis_model_fixed_time)
#type = "response" to get the estimated probabilities
main_analysis_sd_and_ci_fixed_time <- compute_sd_and_CI(full_df_w_basis_functions_fixed_time, main_analysis_data$prop_dead,
coefficient_values_fixed_time,
p = ncol(full_df_w_basis_functions_fixed_time) - 50)
main_analysis_sd_and_ci_fixed_time
## lb_coef coef_values ub_coef
## (Intercept) 1.942733e-05 2.689875e-05 3.437016e-05
## StateAlaska -8.915125e-06 -4.544863e-07 8.006152e-06
## StateArizona 4.074649e-06 1.056466e-05 1.705466e-05
## StateArkansas -3.522119e-05 -2.812388e-05 -2.102657e-05
## StateCalifornia -3.182303e-05 -2.296838e-05 -1.411373e-05
## StateColorado -1.540614e-05 -7.966278e-06 -5.264136e-07
## StateConnecticut 3.982240e-06 1.233036e-05 2.067849e-05
## StateDelaware 6.618517e-06 2.026181e-05 3.390509e-05
## StateFlorida 9.082273e-06 1.476651e-05 2.045074e-05
## StateGeorgia -1.184259e-05 -6.737520e-06 -1.632450e-06
## StateHawaii -3.925571e-05 -3.118831e-05 -2.312091e-05
## StateIdaho -1.303271e-05 -7.178278e-06 -1.323841e-06
## StateIllinois -4.479242e-06 2.423321e-06 9.325884e-06
## StateIndiana 6.627081e-06 1.231332e-05 1.799956e-05
## StateIowa -3.776189e-05 -3.167392e-05 -2.558595e-05
## StateKansas -2.080300e-05 -1.519561e-05 -9.588212e-06
## StateKentucky 4.987862e-05 5.786783e-05 6.585705e-05
## StateLouisiana 1.503427e-05 2.100942e-05 2.698456e-05
## StateMaine -8.073911e-06 2.150682e-06 1.237528e-05
## StateMaryland -6.062060e-05 -5.344500e-05 -4.626940e-05
## StateMassachusetts 9.652271e-06 1.973098e-05 2.980970e-05
## StateMichigan -6.180377e-06 -5.122307e-07 5.155916e-06
## StateMinnesota -5.227065e-05 -4.436410e-05 -3.645755e-05
## StateMississippi -1.254397e-05 -6.310813e-06 -7.765172e-08
## StateMissouri 3.200968e-06 8.772120e-06 1.434327e-05
## StateMontana -4.651537e-05 -3.690314e-05 -2.729090e-05
## StateNebraska -4.321365e-05 -3.727356e-05 -3.133347e-05
## StateNevada 1.617230e-05 2.441663e-05 3.266096e-05
## StateNew Hampshire 4.892681e-06 1.473038e-05 2.456807e-05
## StateNew Jersey -6.275080e-06 3.229125e-06 1.273333e-05
## StateNew Mexico 3.364025e-05 4.374662e-05 5.385300e-05
## StateNew York -1.767349e-05 -1.106203e-05 -4.450582e-06
## StateNorth Carolina 6.891922e-06 1.176628e-05 1.664063e-05
## StateNorth Dakota -5.190478e-05 -4.406765e-05 -3.623052e-05
## StateOhio 2.948539e-05 4.235447e-05 5.522355e-05
## StateOklahoma 2.275446e-05 3.111254e-05 3.947062e-05
## StateOregon -3.780289e-05 -3.002854e-05 -2.225418e-05
## StatePennsylvania 3.560202e-05 4.395971e-05 5.231739e-05
## StateRhode Island 4.021211e-06 1.389934e-05 2.377747e-05
## StateSouth Carolina 7.170290e-06 1.252918e-05 1.788807e-05
## StateSouth Dakota -4.569666e-05 -3.959801e-05 -3.349937e-05
## StateTennessee 2.739848e-05 3.433253e-05 4.126657e-05
## StateTexas -1.177957e-05 -4.870736e-06 2.038100e-06
## StateUtah -3.448839e-06 3.050429e-06 9.549696e-06
## StateVermont -2.680727e-05 -1.915904e-05 -1.151081e-05
## StateVirginia -8.353641e-06 -3.600273e-06 1.153096e-06
## StateWashington -1.902188e-05 -1.091934e-05 -2.816797e-06
## StateWest Virginia 7.077605e-05 8.856911e-05 1.063622e-04
## StateWisconsin -6.304741e-06 -1.369527e-06 3.565686e-06
## StateWyoming -6.603788e-06 5.619765e-07 7.727741e-06
## factor(Time_Period_ID)2 -9.692754e-06 -9.184054e-07 7.855943e-06
## factor(Time_Period_ID)3 -7.047547e-06 1.446718e-06 9.940982e-06
## factor(Time_Period_ID)4 -5.373015e-06 3.162920e-06 1.169886e-05
## factor(Time_Period_ID)5 8.373942e-08 8.631266e-06 1.717879e-05
## factor(Time_Period_ID)6 1.116986e-06 9.443451e-06 1.776991e-05
## factor(Time_Period_ID)7 6.580302e-06 1.471081e-05 2.284132e-05
## factor(Time_Period_ID)8 6.383961e-06 1.452315e-05 2.266234e-05
## factor(Time_Period_ID)9 9.623193e-06 1.749862e-05 2.537405e-05
## factor(Time_Period_ID)10 9.060379e-06 1.698551e-05 2.491065e-05
## factor(Time_Period_ID)11 1.368192e-05 2.134289e-05 2.900385e-05
## factor(Time_Period_ID)12 1.368767e-05 2.223594e-05 3.078422e-05
## factor(Time_Period_ID)13 2.242234e-05 3.015936e-05 3.789639e-05
## factor(Time_Period_ID)14 2.570222e-05 3.341473e-05 4.112724e-05
## factor(Time_Period_ID)15 2.721862e-05 3.513515e-05 4.305168e-05
## factor(Time_Period_ID)16 2.816967e-05 3.590147e-05 4.363327e-05
## factor(Time_Period_ID)17 3.208377e-05 4.012433e-05 4.816490e-05
## factor(Time_Period_ID)18 3.124511e-05 3.897322e-05 4.670133e-05
## factor(Time_Period_ID)19 3.001830e-05 3.949054e-05 4.896278e-05
## factor(Time_Period_ID)20 3.032985e-05 3.882449e-05 4.731914e-05
## factor(Time_Period_ID)21 3.435043e-05 4.242025e-05 5.049006e-05
## factor(Time_Period_ID)22 3.206191e-05 4.039724e-05 4.873257e-05
## factor(Time_Period_ID)23 4.086600e-05 4.921866e-05 5.757132e-05
## factor(Time_Period_ID)24 3.958479e-05 4.817116e-05 5.675754e-05
## factor(Time_Period_ID)25 3.915444e-05 4.777880e-05 5.640317e-05
## factor(Time_Period_ID)26 3.905132e-05 4.763090e-05 5.621049e-05
## factor(Time_Period_ID)27 4.498689e-05 5.359093e-05 6.219497e-05
## factor(Time_Period_ID)28 4.272095e-05 5.148042e-05 6.023988e-05
## factor(Time_Period_ID)29 4.342132e-05 5.252397e-05 6.162661e-05
## factor(Time_Period_ID)30 4.394029e-05 5.345100e-05 6.296171e-05
## factor(Time_Period_ID)31 5.164047e-05 6.132752e-05 7.101457e-05
## factor(Time_Period_ID)32 5.274482e-05 6.292231e-05 7.309981e-05
## factor(Time_Period_ID)33 6.548020e-05 7.678000e-05 8.807980e-05
## factor(Time_Period_ID)34 6.863541e-05 8.123049e-05 9.382557e-05
## factor(Time_Period_ID)35 7.464630e-05 8.908675e-05 1.035272e-04
## factor(Time_Period_ID)36 7.410766e-05 8.729149e-05 1.004753e-04
## factor(Time_Period_ID)37 7.178644e-05 8.432596e-05 9.686548e-05
## factor(Time_Period_ID)38 6.975402e-05 8.290643e-05 9.605884e-05
## factor(Time_Period_ID)39 7.019997e-05 8.255097e-05 9.490197e-05
## factor(Time_Period_ID)40 7.899652e-05 9.261112e-05 1.062257e-04
## Naloxone_Pharmacy_Yes_Redefined -7.593619e-06 -1.490078e-06 4.613463e-06
## Naloxone_Pharmacy_No_Redefined -6.103208e-06 -1.381355e-06 3.340499e-06
## Medical_Marijuana_Redefined 1.500898e-05 2.002227e-05 2.503556e-05
## Recreational_Marijuana_Redefined -2.730819e-05 -1.896470e-05 -1.062121e-05
## GSL_Redefined 1.774296e-06 6.260311e-06 1.074632e-05
## PDMP_Redefined -1.726427e-05 -1.396633e-05 -1.066840e-05
## Medicaid_Expansion_Redefined 7.892999e-06 1.237642e-05 1.685984e-05
## Intervention_Redefined -3.648105e-06 -3.056590e-07 3.036787e-06
## sd_coef
## (Intercept) 3.811947e-06
## StateAlaska 4.316652e-06
## StateArizona 3.311228e-06
## StateArkansas 3.621075e-06
## StateCalifornia 4.517678e-06
## StateColorado 3.795849e-06
## StateConnecticut 4.259247e-06
## StateDelaware 6.960861e-06
## StateFlorida 2.900120e-06
## StateGeorgia 2.604628e-06
## StateHawaii 4.116019e-06
## StateIdaho 2.986957e-06
## StateIllinois 3.521716e-06
## StateIndiana 2.901142e-06
## StateIowa 3.106108e-06
## StateKansas 2.860916e-06
## StateKentucky 4.076130e-06
## StateLouisiana 3.048543e-06
## StateMaine 5.216629e-06
## StateMaryland 3.661021e-06
## StateMassachusetts 5.142200e-06
## StateMichigan 2.891912e-06
## StateMinnesota 4.033952e-06
## StateMississippi 3.180184e-06
## StateMissouri 2.842424e-06
## StateMontana 4.904200e-06
## StateNebraska 3.030658e-06
## StateNevada 4.206289e-06
## StateNew Hampshire 5.019232e-06
## StateNew Jersey 4.849084e-06
## StateNew Mexico 5.156316e-06
## StateNew York 3.373190e-06
## StateNorth Carolina 2.486916e-06
## StateNorth Dakota 3.998535e-06
## StateOhio 6.565857e-06
## StateOklahoma 4.264327e-06
## StateOregon 3.966506e-06
## StatePennsylvania 4.264124e-06
## StateRhode Island 5.039861e-06
## StateSouth Carolina 2.734127e-06
## StateSouth Dakota 3.111554e-06
## StateTennessee 3.537777e-06
## StateTexas 3.524916e-06
## StateUtah 3.315953e-06
## StateVermont 3.902157e-06
## StateVirginia 2.425188e-06
## StateWashington 4.133950e-06
## StateWest Virginia 9.078091e-06
## StateWisconsin 2.517966e-06
## StateWyoming 3.656002e-06
## factor(Time_Period_ID)2 4.476708e-06
## factor(Time_Period_ID)3 4.333808e-06
## factor(Time_Period_ID)4 4.355069e-06
## factor(Time_Period_ID)5 4.360983e-06
## factor(Time_Period_ID)6 4.248196e-06
## factor(Time_Period_ID)7 4.148219e-06
## factor(Time_Period_ID)8 4.152649e-06
## factor(Time_Period_ID)9 4.018075e-06
## factor(Time_Period_ID)10 4.043436e-06
## factor(Time_Period_ID)11 3.908654e-06
## factor(Time_Period_ID)12 4.361364e-06
## factor(Time_Period_ID)13 3.947461e-06
## factor(Time_Period_ID)14 3.934954e-06
## factor(Time_Period_ID)15 4.039045e-06
## factor(Time_Period_ID)16 3.944795e-06
## factor(Time_Period_ID)17 4.102330e-06
## factor(Time_Period_ID)18 3.942913e-06
## factor(Time_Period_ID)19 4.832778e-06
## factor(Time_Period_ID)20 4.334003e-06
## factor(Time_Period_ID)21 4.117252e-06
## factor(Time_Period_ID)22 4.252720e-06
## factor(Time_Period_ID)23 4.261559e-06
## factor(Time_Period_ID)24 4.380804e-06
## factor(Time_Period_ID)25 4.400185e-06
## factor(Time_Period_ID)26 4.377339e-06
## factor(Time_Period_ID)27 4.389815e-06
## factor(Time_Period_ID)28 4.469113e-06
## factor(Time_Period_ID)29 4.644206e-06
## factor(Time_Period_ID)30 4.852404e-06
## factor(Time_Period_ID)31 4.942374e-06
## factor(Time_Period_ID)32 5.192600e-06
## factor(Time_Period_ID)33 5.765205e-06
## factor(Time_Period_ID)34 6.426063e-06
## factor(Time_Period_ID)35 7.367576e-06
## factor(Time_Period_ID)36 6.726444e-06
## factor(Time_Period_ID)37 6.397712e-06
## factor(Time_Period_ID)38 6.710412e-06
## factor(Time_Period_ID)39 6.301531e-06
## factor(Time_Period_ID)40 6.946221e-06
## Naloxone_Pharmacy_Yes_Redefined 3.114052e-06
## Naloxone_Pharmacy_No_Redefined 2.409109e-06
## Medical_Marijuana_Redefined 2.557800e-06
## Recreational_Marijuana_Redefined 4.256882e-06
## GSL_Redefined 2.288783e-06
## PDMP_Redefined 1.682619e-06
## Medicaid_Expansion_Redefined 2.287460e-06
## Intervention_Redefined 1.705330e-06
Event Study
Model Fitting
#create a formula for the gam model which includes the state effects, smoothed time effects, policy measures,
#the periods before the intervention (excluding 1 period and 34 periods before intervention)
#the intervention period, and the periods after the intervention
formula_event_study_fixed_time <- formula(paste("prop_dead ~ State +
factor(Time_Period_ID) +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +",
paste(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)-2),
function(x)paste("neg_", x, "_pd", sep = "")), collapse = "+"),
"+",
paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_event_study_model_fixed_time<-lm(formula_event_study_fixed_time,
data = sensitivity_anlys_event_study_data)
summary(sensitivity_anlys_event_study_model_fixed_time)
##
## Call:
## lm(formula = formula_event_study_fixed_time, data = sensitivity_anlys_event_study_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.003e-04 -1.170e-05 -1.240e-07 1.090e-05 1.303e-04
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.907e-05 6.564e-06 7.476 1.18e-13 ***
## StateAlaska 1.998e-05 6.873e-06 2.907 0.003696 **
## StateArizona 2.229e-05 5.367e-06 4.153 3.43e-05 ***
## StateArkansas -2.006e-05 5.051e-06 -3.973 7.39e-05 ***
## StateCalifornia -3.474e-05 6.131e-06 -5.666 1.70e-08 ***
## StateColorado 3.005e-06 5.618e-06 0.535 0.592762
## StateConnecticut 1.245e-05 5.003e-06 2.488 0.012923 *
## StateDelaware 4.009e-05 6.603e-06 6.071 1.54e-09 ***
## StateFlorida -1.064e-06 6.058e-06 -0.176 0.860542
## StateGeorgia -2.555e-05 6.454e-06 -3.959 7.81e-05 ***
## StateHawaii -2.821e-05 6.053e-06 -4.662 3.36e-06 ***
## StateIdaho 1.148e-05 6.252e-06 1.836 0.066493 .
## StateIllinois -9.164e-06 5.580e-06 -1.642 0.100721
## StateIndiana 1.741e-05 4.825e-06 3.608 0.000316 ***
## StateIowa -3.869e-05 5.117e-06 -7.561 6.30e-14 ***
## StateKansas -1.617e-05 4.692e-06 -3.446 0.000583 ***
## StateKentucky 6.685e-05 5.095e-06 13.119 < 2e-16 ***
## StateLouisiana 1.262e-05 5.170e-06 2.441 0.014721 *
## StateMaine 7.622e-06 5.281e-06 1.443 0.149083
## StateMaryland -6.648e-05 5.664e-06 -11.738 < 2e-16 ***
## StateMassachusetts 2.074e-05 4.761e-06 4.357 1.39e-05 ***
## StateMichigan -3.460e-06 4.991e-06 -0.693 0.488258
## StateMinnesota -4.472e-05 4.923e-06 -9.084 < 2e-16 ***
## StateMississippi 9.347e-06 5.837e-06 1.601 0.109482
## StateMissouri 2.742e-06 5.067e-06 0.541 0.588448
## StateMontana -4.400e-05 5.384e-06 -8.173 5.54e-16 ***
## StateNebraska -2.520e-05 5.423e-06 -4.647 3.62e-06 ***
## StateNevada 2.225e-05 5.176e-06 4.298 1.81e-05 ***
## StateNew Hampshire 1.920e-05 4.858e-06 3.953 8.01e-05 ***
## StateNew Jersey -9.100e-06 5.637e-06 -1.614 0.106631
## StateNew Mexico 4.972e-05 5.257e-06 9.457 < 2e-16 ***
## StateNew York -1.123e-05 4.837e-06 -2.322 0.020329 *
## StateNorth Carolina 6.032e-06 4.934e-06 1.223 0.221662
## StateNorth Dakota -3.190e-05 5.395e-06 -5.913 3.99e-09 ***
## StateOhio 2.432e-05 6.449e-06 3.771 0.000168 ***
## StateOklahoma 3.991e-05 5.013e-06 7.963 2.93e-15 ***
## StateOregon -2.465e-05 5.279e-06 -4.671 3.22e-06 ***
## StatePennsylvania 2.898e-05 6.030e-06 4.806 1.67e-06 ***
## StateRhode Island 3.009e-05 5.947e-06 5.060 4.61e-07 ***
## StateSouth Carolina 3.160e-05 6.357e-06 4.972 7.25e-07 ***
## StateSouth Dakota -1.975e-05 6.566e-06 -3.008 0.002668 **
## StateTennessee 3.461e-05 4.652e-06 7.441 1.53e-13 ***
## StateTexas -1.812e-05 5.845e-06 -3.101 0.001958 **
## StateUtah -8.579e-07 4.856e-06 -0.177 0.859781
## StateVermont -1.440e-05 4.996e-06 -2.881 0.004007 **
## StateVirginia -1.259e-05 5.251e-06 -2.397 0.016640 *
## StateWashington -8.078e-06 5.277e-06 -1.531 0.126024
## StateWest Virginia 1.014e-04 5.442e-06 18.630 < 2e-16 ***
## StateWisconsin -9.904e-06 5.179e-06 -1.912 0.055983 .
## StateWyoming 4.817e-06 4.754e-06 1.013 0.310987
## factor(Time_Period_ID)2 -1.226e-06 4.294e-06 -0.285 0.775335
## factor(Time_Period_ID)3 -7.060e-07 4.340e-06 -0.163 0.870809
## factor(Time_Period_ID)4 -2.624e-07 4.297e-06 -0.061 0.951315
## factor(Time_Period_ID)5 3.820e-06 4.386e-06 0.871 0.383928
## factor(Time_Period_ID)6 3.189e-06 4.450e-06 0.717 0.473747
## factor(Time_Period_ID)7 7.371e-06 4.491e-06 1.641 0.100931
## factor(Time_Period_ID)8 6.092e-06 4.593e-06 1.326 0.184849
## factor(Time_Period_ID)9 8.252e-06 4.684e-06 1.762 0.078257 .
## factor(Time_Period_ID)10 6.567e-06 4.802e-06 1.368 0.171589
## factor(Time_Period_ID)11 9.902e-06 4.927e-06 2.010 0.044593 *
## factor(Time_Period_ID)12 9.748e-06 5.059e-06 1.927 0.054144 .
## factor(Time_Period_ID)13 1.670e-05 5.200e-06 3.210 0.001348 **
## factor(Time_Period_ID)14 1.854e-05 5.360e-06 3.460 0.000553 ***
## factor(Time_Period_ID)15 1.881e-05 5.507e-06 3.416 0.000650 ***
## factor(Time_Period_ID)16 1.899e-05 5.659e-06 3.356 0.000807 ***
## factor(Time_Period_ID)17 2.225e-05 5.855e-06 3.800 0.000150 ***
## factor(Time_Period_ID)18 1.950e-05 6.032e-06 3.233 0.001245 **
## factor(Time_Period_ID)19 1.945e-05 6.206e-06 3.134 0.001751 **
## factor(Time_Period_ID)20 1.735e-05 6.414e-06 2.705 0.006900 **
## factor(Time_Period_ID)21 1.963e-05 6.612e-06 2.969 0.003027 **
## factor(Time_Period_ID)22 1.700e-05 6.804e-06 2.498 0.012578 *
## factor(Time_Period_ID)23 2.441e-05 7.016e-06 3.479 0.000515 ***
## factor(Time_Period_ID)24 2.277e-05 7.230e-06 3.149 0.001662 **
## factor(Time_Period_ID)25 2.236e-05 7.438e-06 3.006 0.002680 **
## factor(Time_Period_ID)26 2.074e-05 7.653e-06 2.710 0.006783 **
## factor(Time_Period_ID)27 2.614e-05 7.869e-06 3.322 0.000911 ***
## factor(Time_Period_ID)28 2.343e-05 8.087e-06 2.898 0.003805 **
## factor(Time_Period_ID)29 2.232e-05 8.412e-06 2.653 0.008038 **
## factor(Time_Period_ID)30 2.271e-05 8.657e-06 2.624 0.008772 **
## factor(Time_Period_ID)31 2.929e-05 8.898e-06 3.292 0.001015 **
## factor(Time_Period_ID)32 2.949e-05 9.193e-06 3.208 0.001360 **
## factor(Time_Period_ID)33 4.277e-05 9.468e-06 4.517 6.66e-06 ***
## factor(Time_Period_ID)34 4.539e-05 9.764e-06 4.648 3.59e-06 ***
## factor(Time_Period_ID)35 5.177e-05 9.984e-06 5.185 2.39e-07 ***
## factor(Time_Period_ID)36 4.976e-05 1.026e-05 4.850 1.34e-06 ***
## factor(Time_Period_ID)37 4.494e-05 1.049e-05 4.285 1.92e-05 ***
## factor(Time_Period_ID)38 4.171e-05 1.073e-05 3.888 0.000105 ***
## factor(Time_Period_ID)39 4.081e-05 1.098e-05 3.716 0.000209 ***
## factor(Time_Period_ID)40 4.924e-05 1.120e-05 4.395 1.17e-05 ***
## Naloxone_Pharmacy_Yes_Redefined -1.607e-06 3.116e-06 -0.516 0.606125
## Naloxone_Pharmacy_No_Redefined -2.293e-06 2.654e-06 -0.864 0.387651
## Medical_Marijuana_Redefined 1.771e-05 2.116e-06 8.371 < 2e-16 ***
## Recreational_Marijuana_Redefined -2.063e-05 3.176e-06 -6.496 1.06e-10 ***
## GSL_Redefined 7.828e-06 2.209e-06 3.545 0.000403 ***
## PDMP_Redefined -1.628e-05 1.773e-06 -9.183 < 2e-16 ***
## Medicaid_Expansion_Redefined 1.417e-05 2.183e-06 6.491 1.09e-10 ***
## neg_2_pd -6.703e-07 4.323e-06 -0.155 0.876786
## neg_3_pd -1.008e-06 4.398e-06 -0.229 0.818725
## neg_4_pd -4.528e-06 4.454e-06 -1.017 0.309477
## neg_5_pd -7.417e-06 4.513e-06 -1.643 0.100464
## neg_6_pd -8.528e-06 4.666e-06 -1.828 0.067732 .
## neg_7_pd -1.275e-05 4.728e-06 -2.696 0.007081 **
## neg_8_pd -1.567e-05 4.847e-06 -3.233 0.001246 **
## neg_9_pd -1.311e-05 5.036e-06 -2.603 0.009329 **
## neg_10_pd -1.458e-05 5.190e-06 -2.809 0.005023 **
## neg_11_pd -1.527e-05 5.354e-06 -2.852 0.004398 **
## neg_12_pd -1.346e-05 5.651e-06 -2.383 0.017296 *
## neg_13_pd -1.744e-05 5.789e-06 -3.012 0.002631 **
## neg_14_pd -1.934e-05 5.941e-06 -3.255 0.001153 **
## neg_15_pd -2.439e-05 6.081e-06 -4.011 6.30e-05 ***
## neg_16_pd -2.572e-05 6.361e-06 -4.044 5.47e-05 ***
## neg_17_pd -2.762e-05 6.771e-06 -4.080 4.71e-05 ***
## neg_18_pd -2.993e-05 6.988e-06 -4.283 1.94e-05 ***
## neg_19_pd -3.146e-05 7.204e-06 -4.367 1.33e-05 ***
## neg_20_pd -3.532e-05 7.647e-06 -4.619 4.13e-06 ***
## neg_21_pd -3.583e-05 8.143e-06 -4.400 1.14e-05 ***
## neg_22_pd -3.694e-05 8.297e-06 -4.453 9.00e-06 ***
## neg_23_pd -3.407e-05 8.606e-06 -3.959 7.80e-05 ***
## neg_24_pd -3.829e-05 9.272e-06 -4.129 3.81e-05 ***
## neg_25_pd -3.708e-05 9.431e-06 -3.932 8.76e-05 ***
## neg_26_pd -3.563e-05 9.804e-06 -3.634 0.000287 ***
## neg_27_pd -3.538e-05 1.093e-05 -3.237 0.001230 **
## neg_28_pd -3.613e-05 1.108e-05 -3.261 0.001130 **
## neg_29_pd -3.344e-05 1.173e-05 -2.851 0.004406 **
## neg_30_pd -3.654e-05 1.252e-05 -2.918 0.003562 **
## neg_31_pd -3.942e-05 1.266e-05 -3.113 0.001880 **
## neg_32_pd -4.412e-05 1.367e-05 -3.227 0.001271 **
## neg_33_pd -3.873e-05 1.737e-05 -2.229 0.025943 *
## pos_0_pd 5.034e-07 4.305e-06 0.117 0.906915
## pos_1_pd -5.834e-07 4.349e-06 -0.134 0.893316
## pos_2_pd 3.351e-06 4.369e-06 0.767 0.443194
## pos_3_pd 2.686e-06 4.452e-06 0.603 0.546407
## pos_4_pd 4.165e-06 4.529e-06 0.920 0.357853
## pos_5_pd 2.911e-06 4.621e-06 0.630 0.528715
## pos_6_pd 5.521e-06 4.749e-06 1.163 0.245110
## pos_7_pd 4.642e-06 4.871e-06 0.953 0.340755
## pos_8_pd 4.601e-06 5.063e-06 0.909 0.363596
## pos_9_pd 5.122e-06 5.229e-06 0.979 0.327482
## pos_10_pd 5.693e-06 5.362e-06 1.062 0.288514
## pos_11_pd 6.550e-06 5.546e-06 1.181 0.237761
## pos_12_pd 9.126e-06 5.736e-06 1.591 0.111772
## pos_13_pd 6.685e-06 5.903e-06 1.132 0.257583
## pos_14_pd 9.568e-06 6.146e-06 1.557 0.119695
## pos_15_pd 9.314e-06 6.374e-06 1.461 0.144126
## pos_16_pd 9.564e-06 6.558e-06 1.459 0.144863
## pos_17_pd 1.345e-05 6.826e-06 1.970 0.048991 *
## pos_18_pd 1.669e-05 7.064e-06 2.362 0.018286 *
## pos_19_pd 1.767e-05 7.240e-06 2.440 0.014779 *
## pos_20_pd 1.843e-05 7.535e-06 2.446 0.014522 *
## pos_21_pd 1.837e-05 7.842e-06 2.343 0.019247 *
## pos_22_pd 1.932e-05 8.080e-06 2.391 0.016921 *
## pos_23_pd 1.877e-05 8.342e-06 2.250 0.024536 *
## pos_24_pd 1.212e-05 8.745e-06 1.386 0.165857
## pos_25_pd 1.599e-05 9.122e-06 1.753 0.079809 .
## pos_26_pd 1.866e-05 9.337e-06 1.998 0.045816 *
## pos_27_pd 1.653e-05 9.572e-06 1.727 0.084370 .
## pos_28_pd 2.006e-05 9.773e-06 2.052 0.040267 *
## pos_29_pd 2.107e-05 1.030e-05 2.045 0.040949 *
## pos_30_pd 2.695e-05 1.061e-05 2.540 0.011178 *
## pos_31_pd 3.953e-05 1.096e-05 3.606 0.000319 ***
## pos_32_pd 4.049e-05 1.166e-05 3.474 0.000524 ***
## pos_33_pd 4.292e-05 1.211e-05 3.544 0.000404 ***
## pos_34_pd 4.819e-05 1.232e-05 3.911 9.53e-05 ***
## pos_35_pd 3.798e-05 1.352e-05 2.809 0.005029 **
## pos_36_pd 3.246e-05 1.372e-05 2.366 0.018067 *
## pos_37_pd 5.077e-05 1.528e-05 3.323 0.000908 ***
## pos_38_pd 5.048e-05 1.882e-05 2.682 0.007391 **
## pos_39_pd 4.850e-05 1.898e-05 2.556 0.010672 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.077e-05 on 1832 degrees of freedom
## Multiple R-squared: 0.8104, Adjusted R-squared: 0.7931
## F-statistic: 46.89 on 167 and 1832 DF, p-value: < 2.2e-16
Sandwich Estimator
#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_event_study_fixed_time <- model.matrix(sensitivity_anlys_event_study_model_fixed_time)
#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_event_study_fixed_time <- coef(sensitivity_anlys_event_study_model_fixed_time)
#type = "response" to get the estimated probabilities
sensitivity_anlys_event_study_sd_and_ci_fixed_time <-
compute_sd_and_CI((full_df_w_basis_functions_sensitivity_anlys_event_study_fixed_time),
sensitivity_anlys_event_study_data$prop_dead,
coefficient_values_sensitivity_anlys_event_study_fixed_time,
p = ncol(full_df_w_basis_functions_sensitivity_anlys_event_study_fixed_time) - 50)
(sensitivity_anlys_event_study_sd_and_ci_fixed_time)
## lb_coef coef_values ub_coef
## (Intercept) 3.918940e-05 4.907266e-05 5.895592e-05
## StateAlaska 9.415737e-06 1.997777e-05 3.053979e-05
## StateArizona 1.475688e-05 2.228880e-05 2.982073e-05
## StateArkansas -2.729612e-05 -2.006447e-05 -1.283281e-05
## StateCalifornia -4.438921e-05 -3.473672e-05 -2.508422e-05
## StateColorado -5.143242e-06 3.005253e-06 1.115375e-05
## StateConnecticut 3.849098e-06 1.244969e-05 2.105028e-05
## StateDelaware 2.544578e-05 4.008813e-05 5.473047e-05
## StateFlorida -8.585087e-06 -1.064421e-06 6.456245e-06
## StateGeorgia -3.377383e-05 -2.555180e-05 -1.732977e-05
## StateHawaii -3.577339e-05 -2.821460e-05 -2.065581e-05
## StateIdaho 2.987889e-06 1.148011e-05 1.997232e-05
## StateIllinois -1.676018e-05 -9.163881e-06 -1.567580e-06
## StateIndiana 1.175833e-05 1.741093e-05 2.306353e-05
## StateIowa -4.515825e-05 -3.869201e-05 -3.222577e-05
## StateKansas -2.184681e-05 -1.616568e-05 -1.048454e-05
## StateKentucky 5.919587e-05 6.684508e-05 7.449429e-05
## StateLouisiana 5.699910e-06 1.262372e-05 1.954753e-05
## StateMaine -3.068301e-06 7.622034e-06 1.831237e-05
## StateMaryland -7.455772e-05 -6.648083e-05 -5.840394e-05
## StateMassachusetts 1.055637e-05 2.074040e-05 3.092442e-05
## StateMichigan -9.237121e-06 -3.460048e-06 2.317025e-06
## StateMinnesota -5.255285e-05 -4.471538e-05 -3.687791e-05
## StateMississippi 9.706533e-07 9.347470e-06 1.772429e-05
## StateMissouri -3.669987e-06 2.742331e-06 9.154649e-06
## StateMontana -5.313471e-05 -4.400468e-05 -3.487465e-05
## StateNebraska -3.217980e-05 -2.519839e-05 -1.821698e-05
## StateNevada 1.405321e-05 2.224755e-05 3.044190e-05
## StateNew Hampshire 8.767847e-06 1.920309e-05 2.963832e-05
## StateNew Jersey -1.857314e-05 -9.100416e-06 3.723078e-07
## StateNew Mexico 3.924470e-05 4.971824e-05 6.019177e-05
## StateNew York -1.782060e-05 -1.123309e-05 -4.645575e-06
## StateNorth Carolina 2.615187e-07 6.031550e-06 1.180158e-05
## StateNorth Dakota -4.091613e-05 -3.190138e-05 -2.288664e-05
## StateOhio 1.081251e-05 2.431685e-05 3.782118e-05
## StateOklahoma 3.170529e-05 3.991344e-05 4.812160e-05
## StateOregon -3.257634e-05 -2.465486e-05 -1.673338e-05
## StatePennsylvania 2.001744e-05 2.897951e-05 3.794158e-05
## StateRhode Island 2.006083e-05 3.009142e-05 4.012200e-05
## StateSouth Carolina 2.383466e-05 3.160438e-05 3.937411e-05
## StateSouth Dakota -2.884540e-05 -1.974829e-05 -1.065118e-05
## StateTennessee 2.743183e-05 3.461431e-05 4.179679e-05
## StateTexas -2.637065e-05 -1.812418e-05 -9.877717e-06
## StateUtah -7.773335e-06 -8.578891e-07 6.057557e-06
## StateVermont -2.224538e-05 -1.439544e-05 -6.545498e-06
## StateVirginia -1.826035e-05 -1.258611e-05 -6.911877e-06
## StateWashington -1.623379e-05 -8.077755e-06 7.827891e-08
## StateWest Virginia 8.395092e-05 1.013932e-04 1.188355e-04
## StateWisconsin -1.612556e-05 -9.903718e-06 -3.681872e-06
## StateWyoming -2.239013e-06 4.817337e-06 1.187369e-05
## factor(Time_Period_ID)2 -9.597072e-06 -1.225815e-06 7.145441e-06
## factor(Time_Period_ID)3 -9.034921e-06 -7.059669e-07 7.622988e-06
## factor(Time_Period_ID)4 -8.615946e-06 -2.624190e-07 8.091108e-06
## factor(Time_Period_ID)5 -4.506297e-06 3.820036e-06 1.214637e-05
## factor(Time_Period_ID)6 -5.223238e-06 3.188753e-06 1.160074e-05
## factor(Time_Period_ID)7 -9.211372e-07 7.371229e-06 1.566360e-05
## factor(Time_Period_ID)8 -2.188981e-06 6.092335e-06 1.437365e-05
## factor(Time_Period_ID)9 1.018667e-07 8.252087e-06 1.640231e-05
## factor(Time_Period_ID)10 -1.638393e-06 6.567047e-06 1.477249e-05
## factor(Time_Period_ID)11 1.794641e-06 9.902275e-06 1.800991e-05
## factor(Time_Period_ID)12 7.328195e-07 9.748255e-06 1.876369e-05
## factor(Time_Period_ID)13 8.436350e-06 1.669515e-05 2.495395e-05
## factor(Time_Period_ID)14 1.005424e-05 1.854409e-05 2.703394e-05
## factor(Time_Period_ID)15 1.006564e-05 1.881056e-05 2.755549e-05
## factor(Time_Period_ID)16 1.031699e-05 1.899209e-05 2.766720e-05
## factor(Time_Period_ID)17 1.313487e-05 2.224645e-05 3.135803e-05
## factor(Time_Period_ID)18 1.056200e-05 1.950250e-05 2.844301e-05
## factor(Time_Period_ID)19 8.924215e-06 1.944967e-05 2.997513e-05
## factor(Time_Period_ID)20 7.440136e-06 1.734689e-05 2.725364e-05
## factor(Time_Period_ID)21 9.955337e-06 1.962960e-05 2.930387e-05
## factor(Time_Period_ID)22 6.878352e-06 1.699581e-05 2.711326e-05
## factor(Time_Period_ID)23 1.412365e-05 2.440944e-05 3.469523e-05
## factor(Time_Period_ID)24 1.217110e-05 2.277040e-05 3.336970e-05
## factor(Time_Period_ID)25 1.141998e-05 2.236039e-05 3.330081e-05
## factor(Time_Period_ID)26 9.762115e-06 2.074361e-05 3.172510e-05
## factor(Time_Period_ID)27 1.504140e-05 2.614184e-05 3.724228e-05
## factor(Time_Period_ID)28 1.193650e-05 2.343302e-05 3.492953e-05
## factor(Time_Period_ID)29 1.005025e-05 2.231965e-05 3.458905e-05
## factor(Time_Period_ID)30 1.004200e-05 2.271297e-05 3.538394e-05
## factor(Time_Period_ID)31 1.626465e-05 2.928890e-05 4.231315e-05
## factor(Time_Period_ID)32 1.612087e-05 2.948974e-05 4.285861e-05
## factor(Time_Period_ID)33 2.854000e-05 4.276776e-05 5.699551e-05
## factor(Time_Period_ID)34 3.038392e-05 4.538755e-05 6.039118e-05
## factor(Time_Period_ID)35 3.495050e-05 5.177306e-05 6.859562e-05
## factor(Time_Period_ID)36 3.310792e-05 4.976202e-05 6.641612e-05
## factor(Time_Period_ID)37 2.862394e-05 4.493881e-05 6.125369e-05
## factor(Time_Period_ID)38 2.477892e-05 4.171212e-05 5.864532e-05
## factor(Time_Period_ID)39 2.419129e-05 4.081074e-05 5.743019e-05
## factor(Time_Period_ID)40 3.164309e-05 4.924131e-05 6.683954e-05
## Naloxone_Pharmacy_Yes_Redefined -7.581728e-06 -1.606767e-06 4.368193e-06
## Naloxone_Pharmacy_No_Redefined -7.127586e-06 -2.293341e-06 2.540904e-06
## Medical_Marijuana_Redefined 1.275663e-05 1.771347e-05 2.267031e-05
## Recreational_Marijuana_Redefined -2.935318e-05 -2.062864e-05 -1.190411e-05
## GSL_Redefined 3.312642e-06 7.828262e-06 1.234388e-05
## PDMP_Redefined -1.969320e-05 -1.628279e-05 -1.287237e-05
## Medicaid_Expansion_Redefined 9.533622e-06 1.417017e-05 1.880671e-05
## neg_2_pd -6.274166e-06 -6.703184e-07 4.933529e-06
## neg_3_pd -7.000043e-06 -1.008170e-06 4.983703e-06
## neg_4_pd -1.086181e-05 -4.527959e-06 1.805890e-06
## neg_5_pd -1.308077e-05 -7.416487e-06 -1.752199e-06
## neg_6_pd -1.450445e-05 -8.528134e-06 -2.551819e-06
## neg_7_pd -1.954347e-05 -1.274767e-05 -5.951873e-06
## neg_8_pd -2.430201e-05 -1.567091e-05 -7.039804e-06
## neg_9_pd -2.003909e-05 -1.310695e-05 -6.174822e-06
## neg_10_pd -2.177931e-05 -1.457926e-05 -7.379218e-06
## neg_11_pd -2.248824e-05 -1.526717e-05 -8.046107e-06
## neg_12_pd -2.156156e-05 -1.346421e-05 -5.366868e-06
## neg_13_pd -2.528649e-05 -1.743717e-05 -9.587852e-06
## neg_14_pd -2.854592e-05 -1.934006e-05 -1.013419e-05
## neg_15_pd -3.495990e-05 -2.438819e-05 -1.381648e-05
## neg_16_pd -3.473324e-05 -2.572456e-05 -1.671589e-05
## neg_17_pd -3.728714e-05 -2.762348e-05 -1.795982e-05
## neg_18_pd -3.984804e-05 -2.992887e-05 -2.000971e-05
## neg_19_pd -4.213891e-05 -3.146036e-05 -2.078180e-05
## neg_20_pd -4.688289e-05 -3.532104e-05 -2.375919e-05
## neg_21_pd -4.878762e-05 -3.583009e-05 -2.287256e-05
## neg_22_pd -5.289732e-05 -3.694092e-05 -2.098452e-05
## neg_23_pd -4.978031e-05 -3.407397e-05 -1.836763e-05
## neg_24_pd -5.637912e-05 -3.828529e-05 -2.019147e-05
## neg_25_pd -5.742895e-05 -3.707766e-05 -1.672636e-05
## neg_26_pd -5.904283e-05 -3.562540e-05 -1.220798e-05
## neg_27_pd -5.328433e-05 -3.538294e-05 -1.748154e-05
## neg_28_pd -5.329725e-05 -3.613286e-05 -1.896847e-05
## neg_29_pd -4.903661e-05 -3.344293e-05 -1.784926e-05
## neg_30_pd -5.296250e-05 -3.654051e-05 -2.011851e-05
## neg_31_pd -5.623422e-05 -3.942031e-05 -2.260640e-05
## neg_32_pd -6.287718e-05 -4.412086e-05 -2.536454e-05
## neg_33_pd -6.760776e-05 -3.872554e-05 -9.843312e-06
## pos_0_pd -5.320048e-06 5.034363e-07 6.326921e-06
## pos_1_pd -7.284032e-06 -5.833719e-07 6.117288e-06
## pos_2_pd -3.260502e-06 3.350705e-06 9.961911e-06
## pos_3_pd -4.355226e-06 2.685961e-06 9.727149e-06
## pos_4_pd -3.656354e-06 4.165419e-06 1.198719e-05
## pos_5_pd -4.508676e-06 2.911528e-06 1.033173e-05
## pos_6_pd -3.001597e-06 5.521126e-06 1.404385e-05
## pos_7_pd -3.360018e-06 4.641613e-06 1.264325e-05
## pos_8_pd -4.432811e-06 4.601253e-06 1.363532e-05
## pos_9_pd -2.883241e-06 5.122046e-06 1.312733e-05
## pos_10_pd -2.563565e-06 5.692585e-06 1.394873e-05
## pos_11_pd -1.614462e-06 6.549633e-06 1.471373e-05
## pos_12_pd 1.224820e-06 9.126041e-06 1.702726e-05
## pos_13_pd -2.597916e-06 6.685110e-06 1.596814e-05
## pos_14_pd 1.014850e-06 9.568026e-06 1.812120e-05
## pos_15_pd -5.288352e-07 9.313612e-06 1.915606e-05
## pos_16_pd -2.928264e-07 9.564428e-06 1.942168e-05
## pos_17_pd 1.945399e-06 1.344625e-05 2.494709e-05
## pos_18_pd 5.903107e-06 1.668558e-05 2.746806e-05
## pos_19_pd 7.727145e-06 1.766528e-05 2.760341e-05
## pos_20_pd 7.746674e-06 1.843406e-05 2.912145e-05
## pos_21_pd 7.427666e-06 1.837290e-05 2.931813e-05
## pos_22_pd 7.904873e-06 1.931568e-05 3.072649e-05
## pos_23_pd 6.230583e-06 1.877273e-05 3.131487e-05
## pos_24_pd 5.839190e-07 1.212190e-05 2.365987e-05
## pos_25_pd 3.418988e-06 1.598852e-05 2.855806e-05
## pos_26_pd 5.776694e-06 1.866037e-05 3.154406e-05
## pos_27_pd 3.088993e-06 1.652909e-05 2.996919e-05
## pos_28_pd 5.913150e-06 2.005808e-05 3.420302e-05
## pos_29_pd 4.555448e-06 2.106577e-05 3.757608e-05
## pos_30_pd 9.999101e-06 2.694735e-05 4.389561e-05
## pos_31_pd 1.765453e-05 3.953294e-05 6.141135e-05
## pos_32_pd 1.231996e-05 4.049465e-05 6.866934e-05
## pos_33_pd 1.478374e-05 4.292117e-05 7.105860e-05
## pos_34_pd 1.416440e-05 4.818733e-05 8.221026e-05
## pos_35_pd 1.221796e-05 3.797534e-05 6.373273e-05
## pos_36_pd 1.196206e-05 3.246222e-05 5.296239e-05
## pos_37_pd 2.456961e-05 5.077491e-05 7.698020e-05
## pos_38_pd 1.098930e-05 5.047506e-05 8.996082e-05
## pos_39_pd -8.116398e-06 4.850436e-05 1.051251e-04
## sd_coef
## (Intercept) 5.042481e-06
## StateAlaska 5.388790e-06
## StateArizona 3.842818e-06
## StateArkansas 3.689620e-06
## StateCalifornia 4.924741e-06
## StateColorado 4.157395e-06
## StateConnecticut 4.388057e-06
## StateDelaware 7.470584e-06
## StateFlorida 3.837075e-06
## StateGeorgia 4.194913e-06
## StateHawaii 3.856525e-06
## StateIdaho 4.332764e-06
## StateIllinois 3.875664e-06
## StateIndiana 2.883979e-06
## StateIowa 3.299102e-06
## StateKansas 2.898539e-06
## StateKentucky 3.902659e-06
## StateLouisiana 3.532555e-06
## StateMaine 5.454253e-06
## StateMaryland 4.120863e-06
## StateMassachusetts 5.195930e-06
## StateMichigan 2.947486e-06
## StateMinnesota 3.998708e-06
## StateMississippi 4.273886e-06
## StateMissouri 3.271591e-06
## StateMontana 4.658177e-06
## StateNebraska 3.561944e-06
## StateNevada 4.180787e-06
## StateNew Hampshire 5.324101e-06
## StateNew Jersey 4.833022e-06
## StateNew Mexico 5.343640e-06
## StateNew York 3.360975e-06
## StateNorth Carolina 2.943894e-06
## StateNorth Dakota 4.599358e-06
## StateOhio 6.889967e-06
## StateOklahoma 4.187833e-06
## StateOregon 4.041571e-06
## StatePennsylvania 4.572486e-06
## StateRhode Island 5.117645e-06
## StateSouth Carolina 3.964145e-06
## StateSouth Dakota 4.641382e-06
## StateTennessee 3.664531e-06
## StateTexas 4.207381e-06
## StateUtah 3.528289e-06
## StateVermont 4.005073e-06
## StateVirginia 2.895018e-06
## StateWashington 4.161242e-06
## StateWest Virginia 8.899132e-06
## StateWisconsin 3.174411e-06
## StateWyoming 3.600178e-06
## factor(Time_Period_ID)2 4.271049e-06
## factor(Time_Period_ID)3 4.249467e-06
## factor(Time_Period_ID)4 4.262003e-06
## factor(Time_Period_ID)5 4.248129e-06
## factor(Time_Period_ID)6 4.291832e-06
## factor(Time_Period_ID)7 4.230799e-06
## factor(Time_Period_ID)8 4.225161e-06
## factor(Time_Period_ID)9 4.158276e-06
## factor(Time_Period_ID)10 4.186449e-06
## factor(Time_Period_ID)11 4.136548e-06
## factor(Time_Period_ID)12 4.599712e-06
## factor(Time_Period_ID)13 4.213673e-06
## factor(Time_Period_ID)14 4.331555e-06
## factor(Time_Period_ID)15 4.461697e-06
## factor(Time_Period_ID)16 4.426075e-06
## factor(Time_Period_ID)17 4.648766e-06
## factor(Time_Period_ID)18 4.561482e-06
## factor(Time_Period_ID)19 5.370131e-06
## factor(Time_Period_ID)20 5.054466e-06
## factor(Time_Period_ID)21 4.935849e-06
## factor(Time_Period_ID)22 5.161966e-06
## factor(Time_Period_ID)23 5.247851e-06
## factor(Time_Period_ID)24 5.407808e-06
## factor(Time_Period_ID)25 5.581842e-06
## factor(Time_Period_ID)26 5.602802e-06
## factor(Time_Period_ID)27 5.663489e-06
## factor(Time_Period_ID)28 5.865569e-06
## factor(Time_Period_ID)29 6.259897e-06
## factor(Time_Period_ID)30 6.464780e-06
## factor(Time_Period_ID)31 6.645023e-06
## factor(Time_Period_ID)32 6.820853e-06
## factor(Time_Period_ID)33 7.259057e-06
## factor(Time_Period_ID)34 7.654915e-06
## factor(Time_Period_ID)35 8.582940e-06
## factor(Time_Period_ID)36 8.496990e-06
## factor(Time_Period_ID)37 8.323916e-06
## factor(Time_Period_ID)38 8.639389e-06
## factor(Time_Period_ID)39 8.479311e-06
## factor(Time_Period_ID)40 8.978687e-06
## Naloxone_Pharmacy_Yes_Redefined 3.048449e-06
## Naloxone_Pharmacy_No_Redefined 2.466452e-06
## Medical_Marijuana_Redefined 2.528999e-06
## Recreational_Marijuana_Redefined 4.451295e-06
## GSL_Redefined 2.303888e-06
## PDMP_Redefined 1.740010e-06
## Medicaid_Expansion_Redefined 2.365584e-06
## neg_2_pd 2.859106e-06
## neg_3_pd 3.057078e-06
## neg_4_pd 3.231555e-06
## neg_5_pd 2.889942e-06
## neg_6_pd 3.049140e-06
## neg_7_pd 3.467244e-06
## neg_8_pd 4.403624e-06
## neg_9_pd 3.536802e-06
## neg_10_pd 3.673492e-06
## neg_11_pd 3.684217e-06
## neg_12_pd 4.131299e-06
## neg_13_pd 4.004753e-06
## neg_14_pd 4.696871e-06
## neg_15_pd 5.393730e-06
## neg_16_pd 4.596263e-06
## neg_17_pd 4.930439e-06
## neg_18_pd 5.060800e-06
## neg_19_pd 5.448243e-06
## neg_20_pd 5.898902e-06
## neg_21_pd 6.610985e-06
## neg_22_pd 8.141021e-06
## neg_23_pd 8.013439e-06
## neg_24_pd 9.231543e-06
## neg_25_pd 1.038331e-05
## neg_26_pd 1.194766e-05
## neg_27_pd 9.133365e-06
## neg_28_pd 8.757342e-06
## neg_29_pd 7.955958e-06
## neg_30_pd 8.378570e-06
## neg_31_pd 8.578524e-06
## neg_32_pd 9.569551e-06
## neg_33_pd 1.473583e-05
## pos_0_pd 2.971165e-06
## pos_1_pd 3.418704e-06
## pos_2_pd 3.373065e-06
## pos_3_pd 3.592443e-06
## pos_4_pd 3.990701e-06
## pos_5_pd 3.785818e-06
## pos_6_pd 4.348328e-06
## pos_7_pd 4.082465e-06
## pos_8_pd 4.609216e-06
## pos_9_pd 4.084330e-06
## pos_10_pd 4.212321e-06
## pos_11_pd 4.165355e-06
## pos_12_pd 4.031235e-06
## pos_13_pd 4.736238e-06
## pos_14_pd 4.363865e-06
## pos_15_pd 5.021657e-06
## pos_16_pd 5.029211e-06
## pos_17_pd 5.867779e-06
## pos_18_pd 5.501263e-06
## pos_19_pd 5.070477e-06
## pos_20_pd 5.452749e-06
## pos_21_pd 5.584302e-06
## pos_22_pd 5.821842e-06
## pos_23_pd 6.399054e-06
## pos_24_pd 5.886723e-06
## pos_25_pd 6.413029e-06
## pos_26_pd 6.573306e-06
## pos_27_pd 6.857193e-06
## pos_28_pd 7.216803e-06
## pos_29_pd 8.423631e-06
## pos_30_pd 8.647068e-06
## pos_31_pd 1.116245e-05
## pos_32_pd 1.437484e-05
## pos_33_pd 1.435583e-05
## pos_34_pd 1.735864e-05
## pos_35_pd 1.314152e-05
## pos_36_pd 1.045927e-05
## pos_37_pd 1.337005e-05
## pos_38_pd 2.014580e-05
## pos_39_pd 2.888814e-05
# write.csv(round(sensitivity_anlys_event_study_sd_and_ci, 3), "./Data/event_study_coef_and_ci.csv")
Plot Results
#plot the coefficients for the periods before and after the intervention with 95% CI
plot_event_study_fixed_time <- sensitivity_anlys_event_study_sd_and_ci_fixed_time %>%
mutate(term = rownames(sensitivity_anlys_event_study_sd_and_ci_fixed_time)) %>%
dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
filter(term %in% c(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2),
function(x){paste("neg_", x, "_pd", sep = "")}),
sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_event_study_fixed_time) <- c("term", "estimate", "conf.low", "conf.high")
dwplot(plot_event_study_fixed_time, colour = "black",
vars_order = c(sapply((max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0,
function(x){paste("pos_", x, "_pd", sep = "")}),
sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2),
function(x){paste("neg_", x, "_pd", sep = "")}))) +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black"),
axis.text.x = element_text(angle = 45)) +
geom_vline(aes(xintercept = 0), linetype = "dashed") +
labs(y = "States Excluded", x = "Coefficients and 95% Confidence Intervals",
title = "Coefficient of Pre-Intervention and Post-Intervention Periods") +
scale_color_grey() +
coord_flip() +
geom_hline(yintercept = 33, col = "red", linetype = "dashed")
Analysis With Only Periods After Treatment
formula_post_tx_fixed_time <- formula(paste("prop_dead~ State +
factor(Time_Period_ID) +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +",
paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_post_tx_model_fixed_time<-lm(formula_post_tx_fixed_time,
data = sensitivity_anlys_event_study_data)
summary(sensitivity_anlys_post_tx_model_fixed_time)
##
## Call:
## lm(formula = formula_post_tx_fixed_time, data = sensitivity_anlys_event_study_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.034e-04 -1.161e-05 8.900e-08 1.119e-05 1.324e-04
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.674e-05 4.473e-06 5.977 2.71e-09 ***
## StateAlaska -3.115e-06 5.329e-06 -0.584 0.558967
## StateArizona 9.139e-06 4.846e-06 1.886 0.059474 .
## StateArkansas -2.964e-05 4.771e-06 -6.212 6.42e-10 ***
## StateCalifornia -1.898e-05 5.387e-06 -3.523 0.000438 ***
## StateColorado -8.754e-06 5.240e-06 -1.671 0.094980 .
## StateConnecticut 1.246e-05 5.015e-06 2.484 0.013061 *
## StateDelaware 1.719e-05 4.924e-06 3.491 0.000493 ***
## StateFlorida 1.769e-05 4.984e-06 3.549 0.000397 ***
## StateGeorgia -4.013e-06 5.096e-06 -0.787 0.431123
## StateHawaii -3.318e-05 5.267e-06 -6.300 3.71e-10 ***
## StateIdaho -9.590e-06 4.818e-06 -1.991 0.046677 *
## StateIllinois 5.085e-06 4.931e-06 1.031 0.302625
## StateIndiana 1.157e-05 4.726e-06 2.449 0.014411 *
## StateIowa -2.884e-05 4.785e-06 -6.028 1.99e-09 ***
## StateKansas -1.454e-05 4.695e-06 -3.097 0.001983 **
## StateKentucky 5.662e-05 4.775e-06 11.857 < 2e-16 ***
## StateLouisiana 2.363e-05 4.755e-06 4.968 7.38e-07 ***
## StateMaine 2.812e-06 5.225e-06 0.538 0.590523
## StateMaryland -5.118e-05 4.925e-06 -10.393 < 2e-16 ***
## StateMassachusetts 2.002e-05 4.773e-06 4.195 2.86e-05 ***
## StateMichigan 2.333e-06 4.875e-06 0.479 0.632270
## StateMinnesota -4.357e-05 4.928e-06 -8.841 < 2e-16 ***
## StateMississippi -8.831e-06 4.760e-06 -1.855 0.063751 .
## StateMissouri 1.041e-05 4.869e-06 2.137 0.032709 *
## StateMontana -3.371e-05 5.030e-06 -6.702 2.71e-11 ***
## StateNebraska -3.919e-05 4.818e-06 -8.135 7.44e-16 ***
## StateNevada 2.739e-05 5.087e-06 5.385 8.16e-08 ***
## StateNew Hampshire 1.380e-05 4.776e-06 2.889 0.003911 **
## StateNew Jersey 5.827e-06 4.929e-06 1.182 0.237323
## StateNew Mexico 4.307e-05 5.142e-06 8.376 < 2e-16 ***
## StateNew York -1.034e-05 4.846e-06 -2.134 0.032946 *
## StateNorth Carolina 1.400e-05 4.712e-06 2.971 0.003008 **
## StateNorth Dakota -4.604e-05 4.771e-06 -9.649 < 2e-16 ***
## StateOhio 4.561e-05 5.114e-06 8.919 < 2e-16 ***
## StateOklahoma 3.044e-05 4.742e-06 6.418 1.74e-10 ***
## StateOregon -3.018e-05 5.200e-06 -5.804 7.60e-09 ***
## StatePennsylvania 4.731e-05 4.997e-06 9.469 < 2e-16 ***
## StateRhode Island 1.209e-05 4.973e-06 2.430 0.015181 *
## StateSouth Carolina 9.715e-06 4.803e-06 2.023 0.043236 *
## StateSouth Dakota -4.267e-05 4.846e-06 -8.806 < 2e-16 ***
## StateTennessee 3.440e-05 4.665e-06 7.374 2.48e-13 ***
## StateTexas -1.227e-06 4.957e-06 -0.248 0.804541
## StateUtah 5.357e-06 4.721e-06 1.135 0.256680
## StateVermont -1.951e-05 4.927e-06 -3.960 7.78e-05 ***
## StateVirginia -7.187e-07 4.778e-06 -0.150 0.880450
## StateWashington -1.075e-05 5.268e-06 -2.040 0.041448 *
## StateWest Virginia 8.687e-05 4.791e-06 18.134 < 2e-16 ***
## StateWisconsin 1.114e-06 4.764e-06 0.234 0.815148
## StateWyoming 3.067e-07 4.697e-06 0.065 0.947943
## factor(Time_Period_ID)2 -8.148e-07 4.170e-06 -0.195 0.845101
## factor(Time_Period_ID)3 1.392e-06 4.169e-06 0.334 0.738528
## factor(Time_Period_ID)4 3.217e-06 4.173e-06 0.771 0.440776
## factor(Time_Period_ID)5 8.682e-06 4.177e-06 2.078 0.037805 *
## factor(Time_Period_ID)6 9.464e-06 4.179e-06 2.265 0.023651 *
## factor(Time_Period_ID)7 1.492e-05 4.186e-06 3.563 0.000375 ***
## factor(Time_Period_ID)8 1.474e-05 4.189e-06 3.519 0.000443 ***
## factor(Time_Period_ID)9 1.788e-05 4.197e-06 4.260 2.14e-05 ***
## factor(Time_Period_ID)10 1.752e-05 4.211e-06 4.161 3.31e-05 ***
## factor(Time_Period_ID)11 2.213e-05 4.221e-06 5.243 1.76e-07 ***
## factor(Time_Period_ID)12 2.307e-05 4.246e-06 5.434 6.25e-08 ***
## factor(Time_Period_ID)13 3.140e-05 4.267e-06 7.358 2.78e-13 ***
## factor(Time_Period_ID)14 3.497e-05 4.291e-06 8.149 6.64e-16 ***
## factor(Time_Period_ID)15 3.682e-05 4.298e-06 8.567 < 2e-16 ***
## factor(Time_Period_ID)16 3.789e-05 4.330e-06 8.751 < 2e-16 ***
## factor(Time_Period_ID)17 4.262e-05 4.374e-06 9.744 < 2e-16 ***
## factor(Time_Period_ID)18 4.134e-05 4.406e-06 9.382 < 2e-16 ***
## factor(Time_Period_ID)19 4.231e-05 4.431e-06 9.548 < 2e-16 ***
## factor(Time_Period_ID)20 4.172e-05 4.478e-06 9.318 < 2e-16 ***
## factor(Time_Period_ID)21 4.550e-05 4.524e-06 10.057 < 2e-16 ***
## factor(Time_Period_ID)22 4.392e-05 4.569e-06 9.613 < 2e-16 ***
## factor(Time_Period_ID)23 5.273e-05 4.613e-06 11.432 < 2e-16 ***
## factor(Time_Period_ID)24 5.216e-05 4.696e-06 11.108 < 2e-16 ***
## factor(Time_Period_ID)25 5.286e-05 4.731e-06 11.173 < 2e-16 ***
## factor(Time_Period_ID)26 5.255e-05 4.790e-06 10.971 < 2e-16 ***
## factor(Time_Period_ID)27 5.909e-05 4.865e-06 12.146 < 2e-16 ***
## factor(Time_Period_ID)28 5.765e-05 4.935e-06 11.682 < 2e-16 ***
## factor(Time_Period_ID)29 5.851e-05 5.027e-06 11.639 < 2e-16 ***
## factor(Time_Period_ID)30 6.016e-05 5.140e-06 11.705 < 2e-16 ***
## factor(Time_Period_ID)31 6.808e-05 5.219e-06 13.044 < 2e-16 ***
## factor(Time_Period_ID)32 6.941e-05 5.442e-06 12.756 < 2e-16 ***
## factor(Time_Period_ID)33 8.387e-05 5.595e-06 14.990 < 2e-16 ***
## factor(Time_Period_ID)34 8.760e-05 5.814e-06 15.066 < 2e-16 ***
## factor(Time_Period_ID)35 9.503e-05 5.915e-06 16.067 < 2e-16 ***
## factor(Time_Period_ID)36 9.429e-05 6.067e-06 15.541 < 2e-16 ***
## factor(Time_Period_ID)37 9.078e-05 6.123e-06 14.825 < 2e-16 ***
## factor(Time_Period_ID)38 8.881e-05 6.218e-06 14.282 < 2e-16 ***
## factor(Time_Period_ID)39 8.921e-05 6.318e-06 14.119 < 2e-16 ***
## factor(Time_Period_ID)40 9.890e-05 6.370e-06 15.527 < 2e-16 ***
## Naloxone_Pharmacy_Yes_Redefined -7.926e-07 3.118e-06 -0.254 0.799383
## Naloxone_Pharmacy_No_Redefined -1.692e-06 2.652e-06 -0.638 0.523627
## Medical_Marijuana_Redefined 1.924e-05 2.101e-06 9.158 < 2e-16 ***
## Recreational_Marijuana_Redefined -1.904e-05 3.170e-06 -6.005 2.29e-09 ***
## GSL_Redefined 7.397e-06 2.211e-06 3.346 0.000837 ***
## PDMP_Redefined -1.482e-05 1.751e-06 -8.466 < 2e-16 ***
## Medicaid_Expansion_Redefined 1.257e-05 2.168e-06 5.795 8.01e-09 ***
## pos_0_pd 1.616e-06 3.289e-06 0.491 0.623357
## pos_1_pd -7.711e-07 3.319e-06 -0.232 0.816302
## pos_2_pd 1.818e-06 3.348e-06 0.543 0.587112
## pos_3_pd -1.410e-07 3.388e-06 -0.042 0.966821
## pos_4_pd 3.618e-08 3.429e-06 0.011 0.991583
## pos_5_pd -2.445e-06 3.481e-06 -0.702 0.482636
## pos_6_pd -1.077e-06 3.548e-06 -0.304 0.761501
## pos_7_pd -3.237e-06 3.612e-06 -0.896 0.370283
## pos_8_pd -4.663e-06 3.724e-06 -1.252 0.210668
## pos_9_pd -5.499e-06 3.804e-06 -1.446 0.148449
## pos_10_pd -6.205e-06 3.856e-06 -1.609 0.107696
## pos_11_pd -6.792e-06 3.942e-06 -1.723 0.085025 .
## pos_12_pd -5.603e-06 4.023e-06 -1.393 0.163892
## pos_13_pd -9.318e-06 4.078e-06 -2.285 0.022422 *
## pos_14_pd -7.893e-06 4.235e-06 -1.864 0.062510 .
## pos_15_pd -9.490e-06 4.340e-06 -2.186 0.028914 *
## pos_16_pd -1.053e-05 4.405e-06 -2.391 0.016921 *
## pos_17_pd -8.141e-06 4.575e-06 -1.779 0.075368 .
## pos_18_pd -6.191e-06 4.688e-06 -1.321 0.186805
## pos_19_pd -6.413e-06 4.752e-06 -1.350 0.177251
## pos_20_pd -7.121e-06 4.956e-06 -1.437 0.150990
## pos_21_pd -8.407e-06 5.170e-06 -1.626 0.104111
## pos_22_pd -8.850e-06 5.298e-06 -1.670 0.095009 .
## pos_23_pd -1.071e-05 5.433e-06 -1.972 0.048749 *
## pos_24_pd -1.860e-05 5.800e-06 -3.207 0.001364 **
## pos_25_pd -1.602e-05 6.141e-06 -2.608 0.009173 **
## pos_26_pd -1.466e-05 6.205e-06 -2.363 0.018217 *
## pos_27_pd -1.828e-05 6.278e-06 -2.911 0.003645 **
## pos_28_pd -1.595e-05 6.360e-06 -2.508 0.012229 *
## pos_29_pd -1.608e-05 6.936e-06 -2.319 0.020517 *
## pos_30_pd -1.151e-05 7.160e-06 -1.608 0.108059
## pos_31_pd -3.809e-07 7.410e-06 -0.051 0.959009
## pos_32_pd -8.162e-07 8.171e-06 -0.100 0.920448
## pos_33_pd 6.965e-08 8.558e-06 0.008 0.993507
## pos_34_pd 4.066e-06 8.628e-06 0.471 0.637521
## pos_35_pd -7.522e-06 1.006e-05 -0.748 0.454706
## pos_36_pd -1.433e-05 1.012e-05 -1.416 0.156930
## pos_37_pd 2.566e-06 1.197e-05 0.214 0.830242
## pos_38_pd 1.193e-06 1.614e-05 0.074 0.941082
## pos_39_pd -2.044e-06 1.619e-05 -0.126 0.899550
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.083e-05 on 1864 degrees of freedom
## Multiple R-squared: 0.806, Adjusted R-squared: 0.7919
## F-statistic: 57.35 on 135 and 1864 DF, p-value: < 2.2e-16
Sandwich Estimator
#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_post_tx_fixed_time <- model.matrix(sensitivity_anlys_post_tx_model_fixed_time)
#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_post_tx_fixed_time <- coef(sensitivity_anlys_post_tx_model_fixed_time)
sensitivity_anlys_post_tx_sd_and_ci_fixed_time <- compute_sd_and_CI((full_df_w_basis_functions_sensitivity_anlys_post_tx_fixed_time),
sensitivity_anlys_event_study_data$prop_dead,
coefficient_values_sensitivity_anlys_post_tx_fixed_time,
p = ncol(full_df_w_basis_functions_sensitivity_anlys_post_tx_fixed_time) - 50)
sensitivity_anlys_post_tx_sd_and_ci_fixed_time
## lb_coef coef_values ub_coef
## (Intercept) 1.926109e-05 2.673763e-05 3.421417e-05
## StateAlaska -1.178898e-05 -3.114563e-06 5.559854e-06
## StateArizona 2.425635e-06 9.138522e-06 1.585141e-05
## StateArkansas -3.653442e-05 -2.963777e-05 -2.274112e-05
## StateCalifornia -2.811939e-05 -1.897606e-05 -9.832728e-06
## StateColorado -1.613416e-05 -8.753872e-06 -1.373581e-06
## StateConnecticut 3.964301e-06 1.246077e-05 2.095723e-05
## StateDelaware 4.690111e-06 1.718974e-05 2.968937e-05
## StateFlorida 1.149270e-05 1.768587e-05 2.387903e-05
## StateGeorgia -1.070454e-05 -4.012762e-06 2.679017e-06
## StateHawaii -4.185938e-05 -3.318200e-05 -2.450463e-05
## StateIdaho -1.600585e-05 -9.590245e-06 -3.174641e-06
## StateIllinois -1.944101e-06 5.084563e-06 1.211323e-05
## StateIndiana 5.917598e-06 1.157477e-05 1.723194e-05
## StateIowa -3.454564e-05 -2.884364e-05 -2.314164e-05
## StateKansas -2.004813e-05 -1.453994e-05 -9.031744e-06
## StateKentucky 4.880712e-05 5.661629e-05 6.442545e-05
## StateLouisiana 1.737451e-05 2.362503e-05 2.987555e-05
## StateMaine -7.666751e-06 2.812057e-06 1.329087e-05
## StateMaryland -5.840156e-05 -5.118158e-05 -4.396159e-05
## StateMassachusetts 9.844275e-06 2.001927e-05 3.019427e-05
## StateMichigan -3.303553e-06 2.333077e-06 7.969707e-06
## StateMinnesota -5.127013e-05 -4.357057e-05 -3.587100e-05
## StateMississippi -1.547806e-05 -8.830505e-06 -2.182946e-06
## StateMissouri 4.492074e-06 1.040698e-05 1.632189e-05
## StateMontana -4.263540e-05 -3.371207e-05 -2.478874e-05
## StateNebraska -4.528139e-05 -3.919208e-05 -3.310276e-05
## StateNevada 1.931649e-05 2.739325e-05 3.547001e-05
## StateNew Hampshire 3.559226e-06 1.379773e-05 2.403624e-05
## StateNew Jersey -2.835253e-06 5.826605e-06 1.448846e-05
## StateNew Mexico 3.303994e-05 4.306669e-05 5.309344e-05
## StateNew York -1.677034e-05 -1.034305e-05 -3.915748e-06
## StateNorth Carolina 8.637619e-06 1.399921e-05 1.936080e-05
## StateNorth Dakota -5.415597e-05 -4.603673e-05 -3.791748e-05
## StateOhio 3.281368e-05 4.560641e-05 5.839915e-05
## StateOklahoma 2.253672e-05 3.043670e-05 3.833668e-05
## StateOregon -3.781999e-05 -3.017922e-05 -2.253845e-05
## StatePennsylvania 3.914230e-05 4.731155e-05 5.548080e-05
## StateRhode Island 2.624633e-06 1.208508e-05 2.154554e-05
## StateSouth Carolina 4.356663e-06 9.714901e-06 1.507314e-05
## StateSouth Dakota -4.941627e-05 -4.267203e-05 -3.592779e-05
## StateTennessee 2.734363e-05 3.440158e-05 4.145954e-05
## StateTexas -8.857649e-06 -1.226835e-06 6.403979e-06
## StateUtah -1.357718e-06 5.357010e-06 1.207174e-05
## StateVermont -2.724877e-05 -1.950978e-05 -1.177079e-05
## StateVirginia -5.815439e-06 -7.187361e-07 4.377967e-06
## StateWashington -1.875728e-05 -1.074987e-05 -2.742465e-06
## StateWest Virginia 6.929496e-05 8.687276e-05 1.044505e-04
## StateWisconsin -4.306579e-06 1.113949e-06 6.534478e-06
## StateWyoming -6.603642e-06 3.067285e-07 7.217099e-06
## factor(Time_Period_ID)2 -9.593816e-06 -8.147579e-07 7.964301e-06
## factor(Time_Period_ID)3 -7.152790e-06 1.391839e-06 9.936467e-06
## factor(Time_Period_ID)4 -5.341024e-06 3.217313e-06 1.177565e-05
## factor(Time_Period_ID)5 1.088454e-07 8.681776e-06 1.725471e-05
## factor(Time_Period_ID)6 1.152168e-06 9.464465e-06 1.777676e-05
## factor(Time_Period_ID)7 6.753696e-06 1.491742e-05 2.308114e-05
## factor(Time_Period_ID)8 6.602689e-06 1.474306e-05 2.288343e-05
## factor(Time_Period_ID)9 9.981193e-06 1.788163e-05 2.578208e-05
## factor(Time_Period_ID)10 9.570509e-06 1.752128e-05 2.547205e-05
## factor(Time_Period_ID)11 1.443397e-05 2.213123e-05 2.982850e-05
## factor(Time_Period_ID)12 1.449619e-05 2.307238e-05 3.164857e-05
## factor(Time_Period_ID)13 2.360748e-05 3.139618e-05 3.918488e-05
## factor(Time_Period_ID)14 2.712613e-05 3.496652e-05 4.280691e-05
## factor(Time_Period_ID)15 2.878928e-05 3.681815e-05 4.484703e-05
## factor(Time_Period_ID)16 3.000808e-05 3.789160e-05 4.577511e-05
## factor(Time_Period_ID)17 3.434205e-05 4.261661e-05 5.089117e-05
## factor(Time_Period_ID)18 3.341175e-05 4.134169e-05 4.927162e-05
## factor(Time_Period_ID)19 3.264751e-05 4.231038e-05 5.197325e-05
## factor(Time_Period_ID)20 3.295743e-05 4.172170e-05 5.048597e-05
## factor(Time_Period_ID)21 3.709225e-05 4.550190e-05 5.391155e-05
## factor(Time_Period_ID)22 3.522925e-05 4.391906e-05 5.260887e-05
## factor(Time_Period_ID)23 4.401627e-05 5.273306e-05 6.144984e-05
## factor(Time_Period_ID)24 4.311571e-05 5.216197e-05 6.120823e-05
## factor(Time_Period_ID)25 4.372822e-05 5.285816e-05 6.198810e-05
## factor(Time_Period_ID)26 4.343225e-05 5.254590e-05 6.165955e-05
## factor(Time_Period_ID)27 4.992913e-05 5.909109e-05 6.825305e-05
## factor(Time_Period_ID)28 4.832476e-05 5.764999e-05 6.697522e-05
## factor(Time_Period_ID)29 4.884542e-05 5.850712e-05 6.816882e-05
## factor(Time_Period_ID)30 5.001869e-05 6.016252e-05 7.030635e-05
## factor(Time_Period_ID)31 5.776697e-05 6.807854e-05 7.839011e-05
## factor(Time_Period_ID)32 5.855183e-05 6.941405e-05 8.027627e-05
## factor(Time_Period_ID)33 7.194099e-05 8.387416e-05 9.580733e-05
## factor(Time_Period_ID)34 7.459926e-05 8.759961e-05 1.006000e-04
## factor(Time_Period_ID)35 7.980179e-05 9.503294e-05 1.102641e-04
## factor(Time_Period_ID)36 7.990080e-05 9.429114e-05 1.086815e-04
## factor(Time_Period_ID)37 7.676103e-05 9.078293e-05 1.048048e-04
## factor(Time_Period_ID)38 7.385274e-05 8.880884e-05 1.037650e-04
## factor(Time_Period_ID)39 7.507232e-05 8.920826e-05 1.033442e-04
## factor(Time_Period_ID)40 8.314134e-05 9.890490e-05 1.146685e-04
## Naloxone_Pharmacy_Yes_Redefined -6.763419e-06 -7.926449e-07 5.178129e-06
## Naloxone_Pharmacy_No_Redefined -6.431447e-06 -1.691816e-06 3.047815e-06
## Medical_Marijuana_Redefined 1.427207e-05 1.923783e-05 2.420359e-05
## Recreational_Marijuana_Redefined -2.758248e-05 -1.903665e-05 -1.049082e-05
## GSL_Redefined 2.918033e-06 7.396887e-06 1.187574e-05
## PDMP_Redefined -1.816936e-05 -1.482011e-05 -1.147086e-05
## Medicaid_Expansion_Redefined 8.025852e-06 1.256512e-05 1.710439e-05
## pos_0_pd -3.179500e-06 1.615661e-06 6.410822e-06
## pos_1_pd -6.564751e-06 -7.711315e-07 5.022488e-06
## pos_2_pd -3.972742e-06 1.818146e-06 7.609033e-06
## pos_3_pd -6.332154e-06 -1.409543e-07 6.050246e-06
## pos_4_pd -6.849249e-06 3.617501e-08 6.921599e-06
## pos_5_pd -9.055662e-06 -2.444664e-06 4.166333e-06
## pos_6_pd -8.678598e-06 -1.077151e-06 6.524296e-06
## pos_7_pd -1.039943e-05 -3.236978e-06 3.925474e-06
## pos_8_pd -1.275496e-05 -4.662586e-06 3.429786e-06
## pos_9_pd -1.263255e-05 -5.499503e-06 1.633548e-06
## pos_10_pd -1.366773e-05 -6.205140e-06 1.257454e-06
## pos_11_pd -1.401242e-05 -6.791952e-06 4.285199e-07
## pos_12_pd -1.250777e-05 -5.603034e-06 1.301704e-06
## pos_13_pd -1.755142e-05 -9.317522e-06 -1.083621e-06
## pos_14_pd -1.542968e-05 -7.893126e-06 -3.565699e-07
## pos_15_pd -1.821065e-05 -9.489572e-06 -7.684925e-07
## pos_16_pd -1.928977e-05 -1.053090e-05 -1.772033e-06
## pos_17_pd -1.873585e-05 -8.140657e-06 2.454532e-06
## pos_18_pd -1.581595e-05 -6.191031e-06 3.433888e-06
## pos_19_pd -1.501200e-05 -6.413490e-06 2.185018e-06
## pos_20_pd -1.634603e-05 -7.120668e-06 2.104691e-06
## pos_21_pd -1.782887e-05 -8.406866e-06 1.015139e-06
## pos_22_pd -1.871128e-05 -8.850347e-06 1.010582e-06
## pos_23_pd -2.188898e-05 -1.071458e-05 4.598232e-07
## pos_24_pd -2.856448e-05 -1.860038e-05 -8.636280e-06
## pos_25_pd -2.700627e-05 -1.601623e-05 -5.026179e-06
## pos_26_pd -2.592827e-05 -1.466370e-05 -3.399140e-06
## pos_27_pd -2.977251e-05 -1.827661e-05 -6.780711e-06
## pos_28_pd -2.843133e-05 -1.594954e-05 -3.467745e-06
## pos_29_pd -3.121158e-05 -1.608384e-05 -9.560911e-07
## pos_30_pd -2.689457e-05 -1.151111e-05 3.872346e-06
## pos_31_pd -2.099949e-05 -3.808817e-07 2.023773e-05
## pos_32_pd -2.786027e-05 -8.161694e-07 2.622793e-05
## pos_33_pd -2.668938e-05 6.965456e-08 2.682869e-05
## pos_34_pd -2.901486e-05 4.065885e-06 3.714663e-05
## pos_35_pd -3.178977e-05 -7.521940e-06 1.674589e-05
## pos_36_pd -3.298920e-05 -1.432901e-05 4.331174e-06
## pos_37_pd -2.257402e-05 2.565877e-06 2.770578e-05
## pos_38_pd -3.728036e-05 1.193187e-06 3.966674e-05
## pos_39_pd -5.796019e-05 -2.043583e-06 5.387302e-05
## sd_coef
## (Intercept) 3.814563e-06
## StateAlaska 4.425723e-06
## StateArizona 3.424942e-06
## StateArkansas 3.518699e-06
## StateCalifornia 4.664966e-06
## StateColorado 3.765454e-06
## StateConnecticut 4.334932e-06
## StateDelaware 6.377363e-06
## StateFlorida 3.159778e-06
## StateGeorgia 3.414173e-06
## StateHawaii 4.427232e-06
## StateIdaho 3.273268e-06
## StateIllinois 3.586053e-06
## StateIndiana 2.886312e-06
## StateIowa 2.909185e-06
## StateKansas 2.810304e-06
## StateKentucky 3.984269e-06
## StateLouisiana 3.189040e-06
## StateMaine 5.346331e-06
## StateMaryland 3.683666e-06
## StateMassachusetts 5.191326e-06
## StateMichigan 2.875832e-06
## StateMinnesota 3.928350e-06
## StateMississippi 3.391612e-06
## StateMissouri 3.017809e-06
## StateMontana 4.552719e-06
## StateNebraska 3.106793e-06
## StateNevada 4.120796e-06
## StateNew Hampshire 5.223727e-06
## StateNew Jersey 4.419316e-06
## StateNew Mexico 5.115691e-06
## StateNew York 3.279234e-06
## StateNorth Carolina 2.735505e-06
## StateNorth Dakota 4.142472e-06
## StateOhio 6.526905e-06
## StateOklahoma 4.030604e-06
## StateOregon 3.898352e-06
## StatePennsylvania 4.167985e-06
## StateRhode Island 4.826761e-06
## StateSouth Carolina 2.733795e-06
## StateSouth Dakota 3.440939e-06
## StateTennessee 3.600999e-06
## StateTexas 3.893272e-06
## StateUtah 3.425881e-06
## StateVermont 3.948464e-06
## StateVirginia 2.600359e-06
## StateWashington 4.085411e-06
## StateWest Virginia 8.968262e-06
## StateWisconsin 2.765576e-06
## StateWyoming 3.525699e-06
## factor(Time_Period_ID)2 4.479111e-06
## factor(Time_Period_ID)3 4.359504e-06
## factor(Time_Period_ID)4 4.366498e-06
## factor(Time_Period_ID)5 4.373944e-06
## factor(Time_Period_ID)6 4.240968e-06
## factor(Time_Period_ID)7 4.165165e-06
## factor(Time_Period_ID)8 4.153250e-06
## factor(Time_Period_ID)9 4.030838e-06
## factor(Time_Period_ID)10 4.056516e-06
## factor(Time_Period_ID)11 3.927176e-06
## factor(Time_Period_ID)12 4.375606e-06
## factor(Time_Period_ID)13 3.973825e-06
## factor(Time_Period_ID)14 4.000199e-06
## factor(Time_Period_ID)15 4.096365e-06
## factor(Time_Period_ID)16 4.022204e-06
## factor(Time_Period_ID)17 4.221713e-06
## factor(Time_Period_ID)18 4.045886e-06
## factor(Time_Period_ID)19 4.930037e-06
## factor(Time_Period_ID)20 4.471565e-06
## factor(Time_Period_ID)21 4.290636e-06
## factor(Time_Period_ID)22 4.433577e-06
## factor(Time_Period_ID)23 4.447340e-06
## factor(Time_Period_ID)24 4.615439e-06
## factor(Time_Period_ID)25 4.658132e-06
## factor(Time_Period_ID)26 4.649822e-06
## factor(Time_Period_ID)27 4.674470e-06
## factor(Time_Period_ID)28 4.757770e-06
## factor(Time_Period_ID)29 4.929440e-06
## factor(Time_Period_ID)30 5.175423e-06
## factor(Time_Period_ID)31 5.261004e-06
## factor(Time_Period_ID)32 5.541948e-06
## factor(Time_Period_ID)33 6.088352e-06
## factor(Time_Period_ID)34 6.632834e-06
## factor(Time_Period_ID)35 7.770996e-06
## factor(Time_Period_ID)36 7.342010e-06
## factor(Time_Period_ID)37 7.154032e-06
## factor(Time_Period_ID)38 7.630668e-06
## factor(Time_Period_ID)39 7.212216e-06
## factor(Time_Period_ID)40 8.042636e-06
## Naloxone_Pharmacy_Yes_Redefined 3.046313e-06
## Naloxone_Pharmacy_No_Redefined 2.418179e-06
## Medical_Marijuana_Redefined 2.533552e-06
## Recreational_Marijuana_Redefined 4.360117e-06
## GSL_Redefined 2.285130e-06
## PDMP_Redefined 1.708801e-06
## Medicaid_Expansion_Redefined 2.315953e-06
## pos_0_pd 2.446511e-06
## pos_1_pd 2.955928e-06
## pos_2_pd 2.954534e-06
## pos_3_pd 3.158775e-06
## pos_4_pd 3.512971e-06
## pos_5_pd 3.372958e-06
## pos_6_pd 3.878289e-06
## pos_7_pd 3.654312e-06
## pos_8_pd 4.128761e-06
## pos_9_pd 3.639312e-06
## pos_10_pd 3.807446e-06
## pos_11_pd 3.683914e-06
## pos_12_pd 3.522826e-06
## pos_13_pd 4.200970e-06
## pos_14_pd 3.845182e-06
## pos_15_pd 4.449530e-06
## pos_16_pd 4.468810e-06
## pos_17_pd 5.405708e-06
## pos_18_pd 4.910673e-06
## pos_19_pd 4.386994e-06
## pos_20_pd 4.706816e-06
## pos_21_pd 4.807146e-06
## pos_22_pd 5.031086e-06
## pos_23_pd 5.701225e-06
## pos_24_pd 5.083725e-06
## pos_25_pd 5.607166e-06
## pos_26_pd 5.747227e-06
## pos_27_pd 5.865254e-06
## pos_28_pd 6.368261e-06
## pos_29_pd 7.718237e-06
## pos_30_pd 7.848702e-06
## pos_31_pd 1.051970e-05
## pos_32_pd 1.379801e-05
## pos_33_pd 1.365257e-05
## pos_34_pd 1.687793e-05
## pos_35_pd 1.238155e-05
## pos_36_pd 9.520503e-06
## pos_37_pd 1.282648e-05
## pos_38_pd 1.962936e-05
## pos_39_pd 2.852888e-05
Plot Results
#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx_fixed_time <- sensitivity_anlys_post_tx_sd_and_ci_fixed_time %>%
mutate(term = rownames(sensitivity_anlys_post_tx_sd_and_ci_fixed_time)) %>%
dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
filter(term %in% c(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_post_tx_fixed_time) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx_fixed_time$num_states <- sapply(plot_post_tx_fixed_time$term, function(x){sum(sensitivity_anlys_event_study_data[,x])})
dwplot(plot_post_tx_fixed_time, colour = "black",
vars_order = c(sapply(((max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0),
function(x){paste("pos_", x, "_pd", sep = "")}))) +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black"),
axis.text.x = element_text(angle = 45, size = 4)) +
geom_vline(aes(xintercept = 0), linetype = "dashed") +
labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals",
title = "Coefficient of Pre-Intervention and Post-Intervention Periods") +
scale_color_grey() +
coord_flip() +
geom_vline(aes(xintercept = coef(main_analysis_model_fixed_time)["Intervention_Redefined"]), linetype = "dashed", color = "red") +
geom_text(aes(label = paste("Coefficient Estimate: ", coef(main_analysis_model_fixed_time)["Intervention_Redefined"]), y = 12,
x = coef(main_analysis_model_fixed_time)["Intervention_Redefined"] + 0.00001), color = "red")
# geom_text(aes(label = num_states, x = .1, y = 40:1), size = 2)
OLS Model Main Analysis With Smoothed Time Effects With Log Proportion
#compute the proportion of people who died from drug overdose
main_analysis_data$prop_dead <- main_analysis_data$imputed_deaths/main_analysis_data$population
#fit an OLS with smoothed time effects
main_analysis_model_log_smoothed_time<-gam(log(prop_dead)~ State +
s(Time_Period_ID, bs = "cr", by = as.factor(Region)) +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +
Intervention_Redefined ,
data = main_analysis_data)
summary(main_analysis_model_log_smoothed_time)
##
## Family: gaussian
## Link function: identity
##
## Formula:
## log(prop_dead) ~ State + s(Time_Period_ID, bs = "cr", by = as.factor(Region)) +
## Naloxone_Pharmacy_Yes_Redefined + Naloxone_Pharmacy_No_Redefined +
## Medical_Marijuana_Redefined + Recreational_Marijuana_Redefined +
## GSL_Redefined + PDMP_Redefined + Medicaid_Expansion_Redefined +
## Intervention_Redefined
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.711293 0.052777 -184.006 < 2e-16 ***
## StateAlaska 0.164106 0.074380 2.206 0.027480 *
## StateArizona 0.288302 0.067744 4.256 2.18e-05 ***
## StateArkansas -0.487283 0.066740 -7.301 4.16e-13 ***
## StateCalifornia -0.155692 0.074371 -2.093 0.036440 *
## StateColorado 0.035981 0.074125 0.485 0.627444
## StateConnecticut 0.230076 0.070893 3.245 0.001193 **
## StateDelaware 0.216431 0.067992 3.183 0.001480 **
## StateFlorida 0.309018 0.066797 4.626 3.97e-06 ***
## StateGeorgia 0.000433 0.066781 0.006 0.994827
## StateHawaii -0.378239 0.072961 -5.184 2.40e-07 ***
## StateIdaho -0.124420 0.066788 -1.863 0.062628 .
## StateIllinois 0.161001 0.067802 2.375 0.017667 *
## StateIndiana 0.081619 0.066357 1.230 0.218845
## StateIowa -0.676997 0.066568 -10.170 < 2e-16 ***
## StateKansas -0.230527 0.066060 -3.490 0.000495 ***
## StateKentucky 0.702316 0.066783 10.516 < 2e-16 ***
## StateLouisiana 0.340740 0.065973 5.165 2.66e-07 ***
## StateMaine 0.088824 0.073874 1.202 0.229369
## StateMaryland -1.513084 0.067786 -22.321 < 2e-16 ***
## StateMassachusetts -0.083599 0.067340 -1.241 0.214593
## StateMichigan 0.010429 0.068383 0.153 0.878801
## StateMinnesota -0.643068 0.069892 -9.201 < 2e-16 ***
## StateMississippi -0.049288 0.066014 -0.747 0.455380
## StateMissouri 0.167659 0.068266 2.456 0.014138 *
## StateMontana -0.439514 0.070271 -6.255 4.90e-10 ***
## StateNebraska -0.874032 0.067084 -13.029 < 2e-16 ***
## StateNevada 0.460178 0.071746 6.414 1.78e-10 ***
## StateNew Hampshire 0.147406 0.067147 2.195 0.028264 *
## StateNew Jersey 0.080613 0.067947 1.186 0.235611
## StateNew Mexico 0.645396 0.072906 8.852 < 2e-16 ***
## StateNew York -0.139492 0.068359 -2.041 0.041429 *
## StateNorth Carolina 0.233840 0.065853 3.551 0.000393 ***
## StateNorth Dakota -1.137555 0.066451 -17.119 < 2e-16 ***
## StateOhio 0.452817 0.066969 6.762 1.80e-11 ***
## StateOklahoma 0.464010 0.066457 6.982 3.99e-12 ***
## StateOregon -0.271552 0.073846 -3.677 0.000242 ***
## StatePennsylvania 0.561023 0.066850 8.392 < 2e-16 ***
## StateRhode Island -0.278774 0.069373 -4.018 6.08e-05 ***
## StateSouth Carolina 0.207544 0.066391 3.126 0.001798 **
## StateSouth Dakota -1.027424 0.066779 -15.386 < 2e-16 ***
## StateTennessee 0.468655 0.065670 7.136 1.35e-12 ***
## StateTexas -0.019383 0.066729 -0.290 0.771481
## StateUtah -0.095477 0.066061 -1.445 0.148542
## StateVermont -0.169566 0.069677 -2.434 0.015041 *
## StateVirginia -0.032103 0.065975 -0.487 0.626602
## StateWashington 0.045026 0.075228 0.599 0.549557
## StateWest Virginia 0.790500 0.066804 11.833 < 2e-16 ***
## StateWisconsin 0.006409 0.066116 0.097 0.922789
## StateWyoming -0.021573 0.066041 -0.327 0.743956
## Naloxone_Pharmacy_Yes_Redefined -0.078516 0.042517 -1.847 0.064946 .
## Naloxone_Pharmacy_No_Redefined -0.001783 0.038500 -0.046 0.963069
## Medical_Marijuana_Redefined 0.192033 0.030656 6.264 4.62e-10 ***
## Recreational_Marijuana_Redefined -0.110335 0.048796 -2.261 0.023863 *
## GSL_Redefined 0.054084 0.031598 1.712 0.087127 .
## PDMP_Redefined -0.152943 0.024680 -6.197 7.02e-10 ***
## Medicaid_Expansion_Redefined 0.091989 0.030149 3.051 0.002311 **
## Intervention_Redefined -0.026254 0.024341 -1.079 0.280903
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(Time_Period_ID):as.factor(Region)Midwest 4.779 5.836 140.15 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)Northeast 8.464 8.917 82.99 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)South 6.300 7.442 105.57 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)West 3.355 4.185 86.33 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.84 Deviance explained = 84.6%
## GCV = 0.089598 Scale est. = 0.085974 n = 2000
gam.check(main_analysis_model_log_smoothed_time, page = 1)
##
## Method: GCV Optimizer: magic
## Smoothing parameter selection converged after 5 iterations.
## The RMS GCV score gradient at convergence was 1.134567e-06 .
## The Hessian was positive definite.
## Model rank = 94 / 94
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(Time_Period_ID):as.factor(Region)Midwest 9.00 4.78 1.05 0.98
## s(Time_Period_ID):as.factor(Region)Northeast 9.00 8.46 1.05 0.98
## s(Time_Period_ID):as.factor(Region)South 9.00 6.30 1.05 0.99
## s(Time_Period_ID):as.factor(Region)West 9.00 3.36 1.05 1.00
#examine fitted values
summary(fitted(main_analysis_model_log_smoothed_time))
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -12.314 -10.207 -9.739 -9.796 -9.341 -8.122
hist(fitted(main_analysis_model_log_smoothed_time))
#smoothed effects
plot(main_analysis_model_log_smoothed_time, pages = 1)
Coefficients and 95% CI
#compute the full dataset including basis functions
full_df_w_basis_functions_log_smoothed_time <- as.matrix(data.frame(predict(main_analysis_model_log_smoothed_time, type = "lpmatrix")))
#estimate the 95% CI and SD
coefficient_values_log_smoothed_time <- coef(main_analysis_model_log_smoothed_time)
#type = "response" to get the estimated probabilities
main_analysis_sd_and_ci_log_smoothed_time <- compute_sd_and_CI(full_df_w_basis_functions_log_smoothed_time,
log(main_analysis_data$prop_dead),
coefficient_values_log_smoothed_time,
p = ncol(full_df_w_basis_functions_log_smoothed_time) - 50)
round(main_analysis_sd_and_ci_log_smoothed_time, 3)
## lb_coef coef_values ub_coef
## (Intercept) -9.800 -9.711 -9.622
## StateAlaska 0.040 0.164 0.289
## StateArizona 0.193 0.288 0.384
## StateArkansas -0.600 -0.487 -0.375
## StateCalifornia -0.274 -0.156 -0.037
## StateColorado -0.074 0.036 0.146
## StateConnecticut 0.097 0.230 0.363
## StateDelaware 0.094 0.216 0.339
## StateFlorida 0.205 0.309 0.413
## StateGeorgia -0.085 0.000 0.086
## StateHawaii -0.496 -0.378 -0.260
## StateIdaho -0.220 -0.124 -0.029
## StateIllinois 0.039 0.161 0.283
## StateIndiana -0.020 0.082 0.183
## StateIowa -0.770 -0.677 -0.584
## StateKansas -0.327 -0.231 -0.134
## StateKentucky 0.616 0.702 0.788
## StateLouisiana 0.248 0.341 0.433
## StateMaine -0.043 0.089 0.221
## StateMaryland -1.719 -1.513 -1.308
## StateMassachusetts -0.297 -0.084 0.129
## StateMichigan -0.083 0.010 0.104
## StateMinnesota -0.746 -0.643 -0.540
## StateMississippi -0.143 -0.049 0.044
## StateMissouri 0.077 0.168 0.259
## StateMontana -0.547 -0.440 -0.332
## StateNebraska -0.969 -0.874 -0.779
## StateNevada 0.349 0.460 0.571
## StateNew Hampshire 0.040 0.147 0.255
## StateNew Jersey -0.075 0.081 0.236
## StateNew Mexico 0.517 0.645 0.774
## StateNew York -0.257 -0.139 -0.022
## StateNorth Carolina 0.154 0.234 0.314
## StateNorth Dakota -1.293 -1.138 -0.982
## StateOhio 0.354 0.453 0.552
## StateOklahoma 0.354 0.464 0.574
## StateOregon -0.382 -0.272 -0.161
## StatePennsylvania 0.456 0.561 0.666
## StateRhode Island -0.581 -0.279 0.023
## StateSouth Carolina 0.119 0.208 0.296
## StateSouth Dakota -1.149 -1.027 -0.906
## StateTennessee 0.388 0.469 0.549
## StateTexas -0.131 -0.019 0.093
## StateUtah -0.258 -0.095 0.067
## StateVermont -0.306 -0.170 -0.033
## StateVirginia -0.127 -0.032 0.062
## StateWashington -0.071 0.045 0.161
## StateWest Virginia 0.650 0.791 0.931
## StateWisconsin -0.075 0.006 0.088
## StateWyoming -0.148 -0.022 0.105
## Naloxone_Pharmacy_Yes_Redefined -0.144 -0.079 -0.013
## Naloxone_Pharmacy_No_Redefined -0.066 -0.002 0.062
## Medical_Marijuana_Redefined 0.125 0.192 0.259
## Recreational_Marijuana_Redefined -0.182 -0.110 -0.039
## GSL_Redefined 0.000 0.054 0.108
## PDMP_Redefined -0.206 -0.153 -0.100
## Medicaid_Expansion_Redefined 0.041 0.092 0.143
## Intervention_Redefined -0.072 -0.026 0.020
## s(Time_Period_ID):as.factor(Region)Midwest.1 -0.542 -0.441 -0.340
## s(Time_Period_ID):as.factor(Region)Midwest.2 -0.249 -0.170 -0.091
## s(Time_Period_ID):as.factor(Region)Midwest.3 0.051 0.135 0.220
## s(Time_Period_ID):as.factor(Region)Midwest.4 0.259 0.343 0.427
## s(Time_Period_ID):as.factor(Region)Midwest.5 0.393 0.473 0.554
## s(Time_Period_ID):as.factor(Region)Midwest.6 0.546 0.625 0.704
## s(Time_Period_ID):as.factor(Region)Midwest.7 0.727 0.806 0.885
## s(Time_Period_ID):as.factor(Region)Midwest.8 0.941 1.032 1.123
## s(Time_Period_ID):as.factor(Region)Midwest.9 0.848 0.944 1.039
## s(Time_Period_ID):as.factor(Region)Northeast.1 -0.777 -0.474 -0.171
## s(Time_Period_ID):as.factor(Region)Northeast.2 -0.527 -0.297 -0.066
## s(Time_Period_ID):as.factor(Region)Northeast.3 0.183 0.362 0.540
## s(Time_Period_ID):as.factor(Region)Northeast.4 0.106 0.279 0.452
## s(Time_Period_ID):as.factor(Region)Northeast.5 0.186 0.359 0.532
## s(Time_Period_ID):as.factor(Region)Northeast.6 0.395 0.553 0.711
## s(Time_Period_ID):as.factor(Region)Northeast.7 0.731 0.895 1.059
## s(Time_Period_ID):as.factor(Region)Northeast.8 1.142 1.314 1.486
## s(Time_Period_ID):as.factor(Region)Northeast.9 0.897 1.050 1.203
## s(Time_Period_ID):as.factor(Region)South.1 -0.426 -0.341 -0.256
## s(Time_Period_ID):as.factor(Region)South.2 -0.159 -0.089 -0.020
## s(Time_Period_ID):as.factor(Region)South.3 0.084 0.166 0.248
## s(Time_Period_ID):as.factor(Region)South.4 0.242 0.319 0.395
## s(Time_Period_ID):as.factor(Region)South.5 0.375 0.441 0.507
## s(Time_Period_ID):as.factor(Region)South.6 0.480 0.549 0.618
## s(Time_Period_ID):as.factor(Region)South.7 0.659 0.736 0.813
## s(Time_Period_ID):as.factor(Region)South.8 0.885 0.992 1.100
## s(Time_Period_ID):as.factor(Region)South.9 0.690 0.827 0.965
## s(Time_Period_ID):as.factor(Region)West.1 -0.373 -0.270 -0.167
## s(Time_Period_ID):as.factor(Region)West.2 -0.163 -0.083 -0.004
## s(Time_Period_ID):as.factor(Region)West.3 0.034 0.115 0.196
## s(Time_Period_ID):as.factor(Region)West.4 0.194 0.263 0.332
## s(Time_Period_ID):as.factor(Region)West.5 0.290 0.362 0.434
## s(Time_Period_ID):as.factor(Region)West.6 0.356 0.438 0.519
## s(Time_Period_ID):as.factor(Region)West.7 0.414 0.503 0.592
## s(Time_Period_ID):as.factor(Region)West.8 0.514 0.626 0.738
## s(Time_Period_ID):as.factor(Region)West.9 0.490 0.588 0.685
## sd_coef
## (Intercept) 0.045
## StateAlaska 0.063
## StateArizona 0.049
## StateArkansas 0.058
## StateCalifornia 0.060
## StateColorado 0.056
## StateConnecticut 0.068
## StateDelaware 0.063
## StateFlorida 0.053
## StateGeorgia 0.044
## StateHawaii 0.060
## StateIdaho 0.049
## StateIllinois 0.062
## StateIndiana 0.052
## StateIowa 0.047
## StateKansas 0.049
## StateKentucky 0.044
## StateLouisiana 0.047
## StateMaine 0.067
## StateMaryland 0.105
## StateMassachusetts 0.109
## StateMichigan 0.048
## StateMinnesota 0.052
## StateMississippi 0.048
## StateMissouri 0.046
## StateMontana 0.055
## StateNebraska 0.048
## StateNevada 0.057
## StateNew Hampshire 0.055
## StateNew Jersey 0.079
## StateNew Mexico 0.065
## StateNew York 0.060
## StateNorth Carolina 0.041
## StateNorth Dakota 0.079
## StateOhio 0.050
## StateOklahoma 0.056
## StateOregon 0.056
## StatePennsylvania 0.054
## StateRhode Island 0.154
## StateSouth Carolina 0.045
## StateSouth Dakota 0.062
## StateTennessee 0.041
## StateTexas 0.057
## StateUtah 0.083
## StateVermont 0.070
## StateVirginia 0.048
## StateWashington 0.059
## StateWest Virginia 0.072
## StateWisconsin 0.042
## StateWyoming 0.064
## Naloxone_Pharmacy_Yes_Redefined 0.034
## Naloxone_Pharmacy_No_Redefined 0.033
## Medical_Marijuana_Redefined 0.034
## Recreational_Marijuana_Redefined 0.036
## GSL_Redefined 0.028
## PDMP_Redefined 0.027
## Medicaid_Expansion_Redefined 0.026
## Intervention_Redefined 0.023
## s(Time_Period_ID):as.factor(Region)Midwest.1 0.052
## s(Time_Period_ID):as.factor(Region)Midwest.2 0.040
## s(Time_Period_ID):as.factor(Region)Midwest.3 0.043
## s(Time_Period_ID):as.factor(Region)Midwest.4 0.043
## s(Time_Period_ID):as.factor(Region)Midwest.5 0.041
## s(Time_Period_ID):as.factor(Region)Midwest.6 0.040
## s(Time_Period_ID):as.factor(Region)Midwest.7 0.040
## s(Time_Period_ID):as.factor(Region)Midwest.8 0.047
## s(Time_Period_ID):as.factor(Region)Midwest.9 0.049
## s(Time_Period_ID):as.factor(Region)Northeast.1 0.155
## s(Time_Period_ID):as.factor(Region)Northeast.2 0.117
## s(Time_Period_ID):as.factor(Region)Northeast.3 0.091
## s(Time_Period_ID):as.factor(Region)Northeast.4 0.088
## s(Time_Period_ID):as.factor(Region)Northeast.5 0.088
## s(Time_Period_ID):as.factor(Region)Northeast.6 0.081
## s(Time_Period_ID):as.factor(Region)Northeast.7 0.084
## s(Time_Period_ID):as.factor(Region)Northeast.8 0.088
## s(Time_Period_ID):as.factor(Region)Northeast.9 0.078
## s(Time_Period_ID):as.factor(Region)South.1 0.043
## s(Time_Period_ID):as.factor(Region)South.2 0.036
## s(Time_Period_ID):as.factor(Region)South.3 0.042
## s(Time_Period_ID):as.factor(Region)South.4 0.039
## s(Time_Period_ID):as.factor(Region)South.5 0.034
## s(Time_Period_ID):as.factor(Region)South.6 0.035
## s(Time_Period_ID):as.factor(Region)South.7 0.039
## s(Time_Period_ID):as.factor(Region)South.8 0.055
## s(Time_Period_ID):as.factor(Region)South.9 0.070
## s(Time_Period_ID):as.factor(Region)West.1 0.053
## s(Time_Period_ID):as.factor(Region)West.2 0.041
## s(Time_Period_ID):as.factor(Region)West.3 0.041
## s(Time_Period_ID):as.factor(Region)West.4 0.035
## s(Time_Period_ID):as.factor(Region)West.5 0.037
## s(Time_Period_ID):as.factor(Region)West.6 0.041
## s(Time_Period_ID):as.factor(Region)West.7 0.046
## s(Time_Period_ID):as.factor(Region)West.8 0.057
## s(Time_Period_ID):as.factor(Region)West.9 0.050
Attributable Deaths
date_data <- main_analysis_data[, c("Time_Period_ID", "Time_Period_Start")]
date_data <- date_data[!duplicated(date_data),]
attr_deaths_est_log_smoothed_time <- attr_death_compute(main_analysis_data, main_analysis_sd_and_ci_log_smoothed_time,
post_tx_model = FALSE, tx_name = "Intervention_Redefined")
attr_deaths_est_log_smoothed_time <- merge(attr_deaths_est_log_smoothed_time, date_data, by.x = "Time_Period", by.y = "Time_Period_ID")
ggplot(attr_deaths_est_log_smoothed_time, aes(x = Time_Period_Start)) +
# geom_point(aes(y = attr_deaths)) +
geom_line(aes(y = attr_deaths, linetype = "Estimate")) +
# geom_point(aes(y = attr_deaths_lb)) +
geom_line(aes(y = attr_deaths_lb, linetype = "95% CI")) +
# geom_point(aes(y = attr_deaths_ub)) +
geom_line(aes(y = attr_deaths_ub, linetype = "95% CI")) +
labs(x = "Date", y = "Attributable Deaths",
title = "Estimated Number of Attributable Deaths Using Smoothed Time Effects,
Log Probability of Drug Overdose Death",
linetype = "") +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black")) +
scale_linetype_manual(values = c("dashed", "solid"))
Event Study
Model Fitting
#create a formula for the gam model which includes the state effects, smoothed time effects, policy measures,
#the periods before the intervention (excluding 1 period and 34 periods before intervention)
#the intervention period, and the periods after the intervention
formula_event_study_log_smoothed_time <- formula(paste("log(prop_dead) ~ State +
s(Time_Period_ID, bs = 'cr', by = as.factor(Region)) +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +",
paste(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)-2),
function(x)paste("neg_", x, "_pd", sep = "")), collapse = "+"),
"+",
paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_event_study_model_log_smoothed_time<-gam(formula_event_study_log_smoothed_time,
data = sensitivity_anlys_event_study_data)
summary(sensitivity_anlys_event_study_model_log_smoothed_time)
##
## Family: gaussian
## Link function: identity
##
## Formula:
## log(prop_dead) ~ State + s(Time_Period_ID, bs = "cr", by = as.factor(Region)) +
## Naloxone_Pharmacy_Yes_Redefined + Naloxone_Pharmacy_No_Redefined +
## Medical_Marijuana_Redefined + Recreational_Marijuana_Redefined +
## GSL_Redefined + PDMP_Redefined + Medicaid_Expansion_Redefined +
## neg_2_pd + neg_3_pd + neg_4_pd + neg_5_pd + neg_6_pd + neg_7_pd +
## neg_8_pd + neg_9_pd + neg_10_pd + neg_11_pd + neg_12_pd +
## neg_13_pd + neg_14_pd + neg_15_pd + neg_16_pd + neg_17_pd +
## neg_18_pd + neg_19_pd + neg_20_pd + neg_21_pd + neg_22_pd +
## neg_23_pd + neg_24_pd + neg_25_pd + neg_26_pd + neg_27_pd +
## neg_28_pd + neg_29_pd + neg_30_pd + neg_31_pd + neg_32_pd +
## neg_33_pd + pos_0_pd + pos_1_pd + pos_2_pd + pos_3_pd + pos_4_pd +
## pos_5_pd + pos_6_pd + pos_7_pd + pos_8_pd + pos_9_pd + pos_10_pd +
## pos_11_pd + pos_12_pd + pos_13_pd + pos_14_pd + pos_15_pd +
## pos_16_pd + pos_17_pd + pos_18_pd + pos_19_pd + pos_20_pd +
## pos_21_pd + pos_22_pd + pos_23_pd + pos_24_pd + pos_25_pd +
## pos_26_pd + pos_27_pd + pos_28_pd + pos_29_pd + pos_30_pd +
## pos_31_pd + pos_32_pd + pos_33_pd + pos_34_pd + pos_35_pd +
## pos_36_pd + pos_37_pd + pos_38_pd + pos_39_pd
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.607755 0.067863 -141.576 < 2e-16 ***
## StateAlaska 0.101715 0.098217 1.036 0.300517
## StateArizona 0.257887 0.075570 3.413 0.000657 ***
## StateArkansas -0.516039 0.070907 -7.278 5.00e-13 ***
## StateCalifornia -0.062450 0.087003 -0.718 0.472974
## StateColorado 0.002447 0.080071 0.031 0.975619
## StateConnecticut 0.222377 0.070209 3.167 0.001563 **
## StateDelaware 0.155066 0.093602 1.657 0.097760 .
## StateFlorida 0.412925 0.085633 4.822 1.54e-06 ***
## StateGeorgia 0.127610 0.091409 1.396 0.162873
## StateHawaii -0.467150 0.085022 -5.494 4.46e-08 ***
## StateIdaho -0.159067 0.088201 -1.803 0.071480 .
## StateIllinois 0.233582 0.078669 2.969 0.003024 **
## StateIndiana 0.076072 0.067464 1.128 0.259638
## StateIowa -0.624313 0.071621 -8.717 < 2e-16 ***
## StateKansas -0.224553 0.065504 -3.428 0.000621 ***
## StateKentucky 0.686996 0.071398 9.622 < 2e-16 ***
## StateLouisiana 0.394888 0.072472 5.449 5.75e-08 ***
## StateMaine 0.074858 0.074340 1.007 0.314085
## StateMaryland -1.451852 0.079818 -18.190 < 2e-16 ***
## StateMassachusetts -0.083063 0.066635 -1.247 0.212728
## StateMichigan 0.050577 0.069988 0.723 0.469989
## StateMinnesota -0.645251 0.069319 -9.308 < 2e-16 ***
## StateMississippi -0.087269 0.082265 -1.061 0.288911
## StateMissouri 0.185703 0.070874 2.620 0.008860 **
## StateMontana -0.394332 0.075905 -5.195 2.27e-07 ***
## StateNebraska -0.912235 0.076218 -11.969 < 2e-16 ***
## StateNevada 0.495673 0.072891 6.800 1.41e-11 ***
## StateNew Hampshire 0.124592 0.068078 1.830 0.067391 .
## StateNew Jersey 0.145728 0.079490 1.833 0.066922 .
## StateNew Mexico 0.622211 0.074154 8.391 < 2e-16 ***
## StateNew York -0.132280 0.067726 -1.953 0.050950 .
## StateNorth Carolina 0.274412 0.069114 3.970 7.45e-05 ***
## StateNorth Dakota -1.172708 0.075925 -15.446 < 2e-16 ***
## StateOhio 0.589152 0.091264 6.455 1.37e-10 ***
## StateOklahoma 0.453117 0.070142 6.460 1.33e-10 ***
## StateOregon -0.299060 0.074811 -3.998 6.65e-05 ***
## StatePennsylvania 0.677460 0.085176 7.954 3.13e-15 ***
## StateRhode Island -0.312528 0.083915 -3.724 0.000202 ***
## StateSouth Carolina 0.161134 0.089821 1.794 0.072984 .
## StateSouth Dakota -1.084871 0.092931 -11.674 < 2e-16 ***
## StateTennessee 0.470730 0.064928 7.250 6.10e-13 ***
## StateTexas 0.087488 0.082520 1.060 0.289191
## StateUtah -0.054042 0.067959 -0.795 0.426594
## StateVermont -0.191088 0.070367 -2.716 0.006677 **
## StateVirginia 0.031406 0.073798 0.426 0.670476
## StateWashington 0.024086 0.075003 0.321 0.748139
## StateWest Virginia 0.763862 0.076548 9.979 < 2e-16 ***
## StateWisconsin 0.055351 0.072662 0.762 0.446302
## StateWyoming -0.026862 0.066431 -0.404 0.685993
## Naloxone_Pharmacy_Yes_Redefined -0.061320 0.042077 -1.457 0.145198
## Naloxone_Pharmacy_No_Redefined 0.003373 0.038423 0.088 0.930048
## Medical_Marijuana_Redefined 0.199071 0.030945 6.433 1.59e-10 ***
## Recreational_Marijuana_Redefined -0.098627 0.049132 -2.007 0.044856 *
## GSL_Redefined 0.063283 0.031502 2.009 0.044694 *
## PDMP_Redefined -0.178714 0.024902 -7.177 1.03e-12 ***
## Medicaid_Expansion_Redefined 0.089196 0.030306 2.943 0.003289 **
## neg_2_pd 0.020525 0.059558 0.345 0.730419
## neg_3_pd 0.016757 0.060521 0.277 0.781904
## neg_4_pd -0.010784 0.061849 -0.174 0.861604
## neg_5_pd -0.013005 0.062636 -0.208 0.835542
## neg_6_pd -0.005779 0.064769 -0.089 0.928918
## neg_7_pd -0.044022 0.065888 -0.668 0.504133
## neg_8_pd -0.100544 0.067553 -1.488 0.136824
## neg_9_pd -0.025159 0.070355 -0.358 0.720682
## neg_10_pd 0.024031 0.072377 0.332 0.739905
## neg_11_pd 0.025412 0.074678 0.340 0.733676
## neg_12_pd 0.115436 0.078970 1.462 0.143974
## neg_13_pd 0.015177 0.080972 0.187 0.851337
## neg_14_pd -0.015730 0.083077 -0.189 0.849848
## neg_15_pd -0.059495 0.085395 -0.697 0.486076
## neg_16_pd -0.043767 0.089648 -0.488 0.625457
## neg_17_pd -0.060151 0.094770 -0.635 0.525694
## neg_18_pd -0.051908 0.098163 -0.529 0.597012
## neg_19_pd -0.154364 0.101364 -1.523 0.127962
## neg_20_pd -0.193711 0.107211 -1.807 0.070952 .
## neg_21_pd -0.117693 0.114201 -1.031 0.302874
## neg_22_pd -0.096424 0.116856 -0.825 0.409392
## neg_23_pd -0.116591 0.121027 -0.963 0.335499
## neg_24_pd -0.180864 0.130018 -1.391 0.164370
## neg_25_pd -0.038789 0.132443 -0.293 0.769652
## neg_26_pd 0.044238 0.138129 0.320 0.748801
## neg_27_pd -0.213628 0.153601 -1.391 0.164454
## neg_28_pd -0.201311 0.156228 -1.289 0.197708
## neg_29_pd 0.024088 0.164854 0.146 0.883844
## neg_30_pd -0.052096 0.175256 -0.297 0.766303
## neg_31_pd -0.054179 0.177815 -0.305 0.760633
## neg_32_pd 0.032863 0.192904 0.170 0.864746
## neg_33_pd 0.109008 0.244825 0.445 0.656193
## pos_0_pd -0.011150 0.059300 -0.188 0.850881
## pos_1_pd -0.040114 0.059907 -0.670 0.503195
## pos_2_pd -0.005207 0.060753 -0.086 0.931707
## pos_3_pd -0.041494 0.061831 -0.671 0.502250
## pos_4_pd -0.047126 0.063088 -0.747 0.455163
## pos_5_pd -0.092046 0.064554 -1.426 0.154073
## pos_6_pd -0.097121 0.066353 -1.464 0.143447
## pos_7_pd -0.094524 0.068293 -1.384 0.166498
## pos_8_pd -0.140579 0.070834 -1.985 0.047333 *
## pos_9_pd -0.162175 0.073212 -2.215 0.026873 *
## pos_10_pd -0.180017 0.075305 -2.390 0.016926 *
## pos_11_pd -0.183783 0.077902 -2.359 0.018419 *
## pos_12_pd -0.193796 0.080631 -2.403 0.016337 *
## pos_13_pd -0.262320 0.083119 -3.156 0.001626 **
## pos_14_pd -0.247336 0.086650 -2.854 0.004359 **
## pos_15_pd -0.250438 0.089880 -2.786 0.005385 **
## pos_16_pd -0.268524 0.092766 -2.895 0.003840 **
## pos_17_pd -0.263062 0.096568 -2.724 0.006508 **
## pos_18_pd -0.253664 0.099917 -2.539 0.011207 *
## pos_19_pd -0.243608 0.102661 -2.373 0.017749 *
## pos_20_pd -0.247583 0.106915 -2.316 0.020683 *
## pos_21_pd -0.274332 0.111178 -2.468 0.013696 *
## pos_22_pd -0.266750 0.114684 -2.326 0.020129 *
## pos_23_pd -0.273338 0.118731 -2.302 0.021437 *
## pos_24_pd -0.310855 0.123993 -2.507 0.012260 *
## pos_25_pd -0.279921 0.129223 -2.166 0.030424 *
## pos_26_pd -0.289984 0.132325 -2.191 0.028544 *
## pos_27_pd -0.338309 0.135880 -2.490 0.012870 *
## pos_28_pd -0.321207 0.138889 -2.313 0.020849 *
## pos_29_pd -0.334409 0.146219 -2.287 0.022306 *
## pos_30_pd -0.285008 0.150706 -1.891 0.058760 .
## pos_31_pd -0.241546 0.155923 -1.549 0.121520
## pos_32_pd -0.298667 0.165839 -1.801 0.071875 .
## pos_33_pd -0.326206 0.172025 -1.896 0.058080 .
## pos_34_pd -0.314276 0.175300 -1.793 0.073169 .
## pos_35_pd -0.514644 0.191451 -2.688 0.007250 **
## pos_36_pd -0.541251 0.194692 -2.780 0.005490 **
## pos_37_pd -0.534988 0.216760 -2.468 0.013673 *
## pos_38_pd -0.513830 0.263987 -1.946 0.051755 .
## pos_39_pd -0.534088 0.267298 -1.998 0.045852 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(Time_Period_ID):as.factor(Region)Midwest 4.324 5.320 41.55 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)Northeast 8.377 8.891 30.51 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)South 5.950 7.101 27.09 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)West 3.005 3.768 28.00 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.844 Deviance explained = 85.5%
## GCV = 0.09088 Scale est. = 0.084034 n = 2000
Sandwich Estimator
#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_event_study_log_smoothed_time <-
data.frame(predict(sensitivity_anlys_event_study_model_log_smoothed_time, type = "lpmatrix"))
#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_event_study_log_smoothed_time <- coef(sensitivity_anlys_event_study_model_log_smoothed_time)
#type = "response" to get the estimated probabilities
sensitivity_anlys_event_study_sd_and_ci_log_smoothed_time <-
compute_sd_and_CI(as.matrix(full_df_w_basis_functions_sensitivity_anlys_event_study_log_smoothed_time),
log(sensitivity_anlys_event_study_data$prop_dead),
coefficient_values_sensitivity_anlys_event_study_log_smoothed_time,
p = ncol(full_df_w_basis_functions_sensitivity_anlys_event_study_log_smoothed_time) - 50)
(sensitivity_anlys_event_study_sd_and_ci_log_smoothed_time)
## lb_coef coef_values
## (Intercept) -9.728823888 -9.607755377
## StateAlaska -0.047405904 0.101715259
## StateArizona 0.146009989 0.257887425
## StateArkansas -0.625065356 -0.516038962
## StateCalifornia -0.195801439 -0.062450464
## StateColorado -0.120135673 0.002447472
## StateConnecticut 0.089301661 0.222377470
## StateDelaware 0.020468319 0.155066167
## StateFlorida 0.294377706 0.412924559
## StateGeorgia 0.013906978 0.127609736
## StateHawaii -0.608365093 -0.467150486
## StateIdaho -0.275351996 -0.159066931
## StateIllinois 0.104812517 0.233581709
## StateIndiana -0.023612076 0.076071921
## StateIowa -0.732961003 -0.624312899
## StateKansas -0.320955862 -0.224552743
## StateKentucky 0.592302264 0.686996193
## StateLouisiana 0.293469508 0.394888461
## StateMaine -0.063869300 0.074857829
## StateMaryland -1.672434093 -1.451851831
## StateMassachusetts -0.299079313 -0.083062578
## StateMichigan -0.045169095 0.050576690
## StateMinnesota -0.753441298 -0.645251331
## StateMississippi -0.209093790 -0.087268616
## StateMissouri 0.086401505 0.185702542
## StateMontana -0.509216034 -0.394331541
## StateNebraska -1.017176026 -0.912234589
## StateNevada 0.385989567 0.495672978
## StateNew Hampshire 0.012195381 0.124591896
## StateNew Jersey -0.008620296 0.145727757
## StateNew Mexico 0.488774253 0.622210509
## StateNew York -0.251050987 -0.132279799
## StateNorth Carolina 0.187299971 0.274412387
## StateNorth Dakota -1.341397313 -1.172707883
## StateOhio 0.455678130 0.589151698
## StateOklahoma 0.337846240 0.453117480
## StateOregon -0.415292220 -0.299059866
## StatePennsylvania 0.561017187 0.677459526
## StateRhode Island -0.586170729 -0.312527565
## StateSouth Carolina 0.046751608 0.161134027
## StateSouth Dakota -1.216535630 -1.084870928
## StateTennessee 0.383486326 0.470729691
## StateTexas -0.032252917 0.087487525
## StateUtah -0.238697614 -0.054041819
## StateVermont -0.333329255 -0.191087648
## StateVirginia -0.067956844 0.031405848
## StateWashington -0.095354561 0.024086450
## StateWest Virginia 0.618242919 0.763862290
## StateWisconsin -0.040024448 0.055350995
## StateWyoming -0.156265025 -0.026862195
## Naloxone_Pharmacy_Yes_Redefined -0.125945151 -0.061319716
## Naloxone_Pharmacy_No_Redefined -0.060956513 0.003373398
## Medical_Marijuana_Redefined 0.129985765 0.199070518
## Recreational_Marijuana_Redefined -0.174441233 -0.098626529
## GSL_Redefined 0.008441128 0.063283495
## PDMP_Redefined -0.233796444 -0.178713621
## Medicaid_Expansion_Redefined 0.038062580 0.089195898
## neg_2_pd -0.090842524 0.020524738
## neg_3_pd -0.093266935 0.016757110
## neg_4_pd -0.130124958 -0.010783798
## neg_5_pd -0.128729866 -0.013004948
## neg_6_pd -0.115563431 -0.005778559
## neg_7_pd -0.159146724 -0.044021509
## neg_8_pd -0.243293082 -0.100544147
## neg_9_pd -0.180033617 -0.025158944
## neg_10_pd -0.117013914 0.024031356
## neg_11_pd -0.123358860 0.025412131
## neg_12_pd -0.047903816 0.115435529
## neg_13_pd -0.150624459 0.015177292
## neg_14_pd -0.172638404 -0.015729613
## neg_15_pd -0.246143938 -0.059495317
## neg_16_pd -0.215163327 -0.043767301
## neg_17_pd -0.211202240 -0.060151411
## neg_18_pd -0.194190577 -0.051908104
## neg_19_pd -0.383178158 -0.154364075
## neg_20_pd -0.446272143 -0.193711115
## neg_21_pd -0.297364419 -0.117692721
## neg_22_pd -0.284965743 -0.096423617
## neg_23_pd -0.398786798 -0.116590871
## neg_24_pd -0.517924064 -0.180864324
## neg_25_pd -0.321229170 -0.038788957
## neg_26_pd -0.301468962 0.044238456
## neg_27_pd -0.707552430 -0.213628304
## neg_28_pd -0.663134057 -0.201311333
## neg_29_pd -0.241917565 0.024088229
## neg_30_pd -0.304155495 -0.052096370
## neg_31_pd -0.274766638 -0.054179201
## neg_32_pd -0.177009269 0.032863102
## neg_33_pd -0.212190787 0.109007659
## pos_0_pd -0.117804387 -0.011149669
## pos_1_pd -0.153952985 -0.040113963
## pos_2_pd -0.109271024 -0.005207113
## pos_3_pd -0.147951769 -0.041493922
## pos_4_pd -0.153750936 -0.047126354
## pos_5_pd -0.200386359 -0.092045551
## pos_6_pd -0.210146623 -0.097121035
## pos_7_pd -0.212953830 -0.094523821
## pos_8_pd -0.253243669 -0.140578750
## pos_9_pd -0.280162923 -0.162175014
## pos_10_pd -0.305299298 -0.180016549
## pos_11_pd -0.300854941 -0.183783467
## pos_12_pd -0.316120292 -0.193795841
## pos_13_pd -0.400921985 -0.262320233
## pos_14_pd -0.386047681 -0.247335909
## pos_15_pd -0.385495339 -0.250438341
## pos_16_pd -0.408108802 -0.268524051
## pos_17_pd -0.404219857 -0.263061724
## pos_18_pd -0.398358676 -0.253663735
## pos_19_pd -0.383498238 -0.243608362
## pos_20_pd -0.396695074 -0.247582690
## pos_21_pd -0.432711692 -0.274332431
## pos_22_pd -0.422558279 -0.266749984
## pos_23_pd -0.437700745 -0.273338184
## pos_24_pd -0.485100733 -0.310854938
## pos_25_pd -0.473288282 -0.279921074
## pos_26_pd -0.478654088 -0.289983620
## pos_27_pd -0.538577534 -0.338308822
## pos_28_pd -0.527526463 -0.321207072
## pos_29_pd -0.551613080 -0.334408979
## pos_30_pd -0.510095934 -0.285008197
## pos_31_pd -0.493354996 -0.241545861
## pos_32_pd -0.545086726 -0.298666643
## pos_33_pd -0.632136706 -0.326206090
## pos_34_pd -0.629075408 -0.314276284
## pos_35_pd -0.786883592 -0.514644392
## pos_36_pd -0.801594573 -0.541250661
## pos_37_pd -0.778573832 -0.534987709
## pos_38_pd -0.752518722 -0.513830174
## pos_39_pd -0.840631968 -0.534088308
## s(Time_Period_ID):as.factor(Region)Midwest.1 -0.604810921 -0.494737079
## s(Time_Period_ID):as.factor(Region)Midwest.2 -0.312013934 -0.224608521
## s(Time_Period_ID):as.factor(Region)Midwest.3 0.006447567 0.093175900
## s(Time_Period_ID):as.factor(Region)Midwest.4 0.248768267 0.333711394
## s(Time_Period_ID):as.factor(Region)Midwest.5 0.430895650 0.513087394
## s(Time_Period_ID):as.factor(Region)Midwest.6 0.614550129 0.703168971
## s(Time_Period_ID):as.factor(Region)Midwest.7 0.811163635 0.903771029
## s(Time_Period_ID):as.factor(Region)Midwest.8 1.041776231 1.159056321
## s(Time_Period_ID):as.factor(Region)Midwest.9 0.972590496 1.099762557
## s(Time_Period_ID):as.factor(Region)Northeast.1 -0.855128818 -0.570605352
## s(Time_Period_ID):as.factor(Region)Northeast.2 -0.575219298 -0.351951731
## s(Time_Period_ID):as.factor(Region)Northeast.3 0.137819821 0.305946250
## s(Time_Period_ID):as.factor(Region)Northeast.4 0.071834695 0.234789810
## s(Time_Period_ID):as.factor(Region)Northeast.5 0.186736401 0.353117285
## s(Time_Period_ID):as.factor(Region)Northeast.6 0.441019976 0.593323854
## s(Time_Period_ID):as.factor(Region)Northeast.7 0.824271871 0.987559759
## s(Time_Period_ID):as.factor(Region)Northeast.8 1.248279088 1.424383187
## s(Time_Period_ID):as.factor(Region)Northeast.9 1.041444149 1.204455894
## s(Time_Period_ID):as.factor(Region)South.1 -0.485631359 -0.389922135
## s(Time_Period_ID):as.factor(Region)South.2 -0.207388443 -0.131694247
## s(Time_Period_ID):as.factor(Region)South.3 0.058850086 0.143187991
## s(Time_Period_ID):as.factor(Region)South.4 0.245225395 0.320084111
## s(Time_Period_ID):as.factor(Region)South.5 0.396570600 0.464161403
## s(Time_Period_ID):as.factor(Region)South.6 0.524700283 0.604633801
## s(Time_Period_ID):as.factor(Region)South.7 0.709248609 0.807908570
## s(Time_Period_ID):as.factor(Region)South.8 0.959164552 1.095942563
## s(Time_Period_ID):as.factor(Region)South.9 0.826912089 0.991245595
## s(Time_Period_ID):as.factor(Region)West.1 -0.427179482 -0.308386528
## s(Time_Period_ID):as.factor(Region)West.2 -0.223790527 -0.131400014
## s(Time_Period_ID):as.factor(Region)West.3 -0.020458926 0.069973226
## s(Time_Period_ID):as.factor(Region)West.4 0.155490954 0.230646763
## s(Time_Period_ID):as.factor(Region)West.5 0.276682349 0.357605994
## s(Time_Period_ID):as.factor(Region)West.6 0.375479806 0.468020533
## s(Time_Period_ID):as.factor(Region)West.7 0.468603452 0.566258884
## s(Time_Period_ID):as.factor(Region)West.8 0.603636187 0.719563215
## s(Time_Period_ID):as.factor(Region)West.9 0.586878298 0.704585511
## ub_coef sd_coef
## (Intercept) -9.4866868669 0.06176965
## StateAlaska 0.2508364222 0.07608223
## StateArizona 0.3697648601 0.05708032
## StateArkansas -0.4070125673 0.05562571
## StateCalifornia 0.0709005101 0.06803621
## StateColorado 0.1250306159 0.06254242
## StateConnecticut 0.3554532799 0.06789582
## StateDelaware 0.2896640143 0.06867237
## StateFlorida 0.5314714116 0.06048309
## StateGeorgia 0.2413124953 0.05801161
## StateHawaii -0.3259358787 0.07204827
## StateIdaho -0.0427818655 0.05932911
## StateIllinois 0.3623509004 0.06569857
## StateIndiana 0.1757559184 0.05085918
## StateIowa -0.5156647960 0.05543271
## StateKansas -0.1281496232 0.04918527
## StateKentucky 0.7816901223 0.04831323
## StateLouisiana 0.4963074142 0.05174436
## StateMaine 0.2135849575 0.07077915
## StateMaryland -1.2312695688 0.11254197
## StateMassachusetts 0.1329541565 0.11021262
## StateMichigan 0.1463224759 0.04884989
## StateMinnesota -0.5370613641 0.05519896
## StateMississippi 0.0345565579 0.06215570
## StateMissouri 0.2850035798 0.05066379
## StateMontana -0.2794470485 0.05861454
## StateNebraska -0.8072931523 0.05354155
## StateNevada 0.6053563884 0.05596092
## StateNew Hampshire 0.2369884117 0.05734516
## StateNew Jersey 0.3000758093 0.07874901
## StateNew Mexico 0.7556467656 0.06807972
## StateNew York -0.0135086105 0.06059754
## StateNorth Carolina 0.3615248024 0.04444511
## StateNorth Dakota -1.0040184526 0.08606604
## StateOhio 0.7226252666 0.06809876
## StateOklahoma 0.5683887208 0.05881186
## StateOregon -0.1828275119 0.05930222
## StatePennsylvania 0.7939018648 0.05940936
## StateRhode Island -0.0388844005 0.13961386
## StateSouth Carolina 0.2755164455 0.05835838
## StateSouth Dakota -0.9532062268 0.06717587
## StateTennessee 0.5579730566 0.04451192
## StateTexas 0.2072279669 0.06109206
## StateUtah 0.1306139757 0.09421214
## StateVermont -0.0488460423 0.07257225
## StateVirginia 0.1307685399 0.05069525
## StateWashington 0.1435274614 0.06093929
## StateWest Virginia 0.9094816603 0.07429560
## StateWisconsin 0.1507264367 0.04866094
## StateWyoming 0.1025406352 0.06602185
## Naloxone_Pharmacy_Yes_Redefined 0.0033057204 0.03297216
## Naloxone_Pharmacy_No_Redefined 0.0677033095 0.03282138
## Medical_Marijuana_Redefined 0.2681552721 0.03524732
## Recreational_Marijuana_Redefined -0.0228118260 0.03868097
## GSL_Redefined 0.1181258621 0.02798080
## PDMP_Redefined -0.1236307979 0.02810348
## Medicaid_Expansion_Redefined 0.1403292147 0.02608843
## neg_2_pd 0.1318919996 0.05682003
## neg_3_pd 0.1267811550 0.05613472
## neg_4_pd 0.1085573626 0.06088835
## neg_5_pd 0.1027199694 0.05904333
## neg_6_pd 0.1040063133 0.05601269
## neg_7_pd 0.0711037058 0.05873735
## neg_8_pd 0.0422047875 0.07283109
## neg_9_pd 0.1297157295 0.07901769
## neg_10_pd 0.1650766271 0.07196187
## neg_11_pd 0.1741831221 0.07590357
## neg_12_pd 0.2787748743 0.08333640
## neg_13_pd 0.1809790428 0.08459273
## neg_14_pd 0.1411791778 0.08005551
## neg_15_pd 0.1271533044 0.09522889
## neg_16_pd 0.1276287244 0.08744695
## neg_17_pd 0.0908994188 0.07706675
## neg_18_pd 0.0903743687 0.07259310
## neg_19_pd 0.0744500090 0.11674188
## neg_20_pd 0.0588499140 0.12885767
## neg_21_pd 0.0619789771 0.09166923
## neg_22_pd 0.0921185097 0.09619496
## neg_23_pd 0.1656050554 0.14397751
## neg_24_pd 0.1561954167 0.17196926
## neg_25_pd 0.2436512570 0.14410215
## neg_26_pd 0.3899458747 0.17638134
## neg_27_pd 0.2802958226 0.25200211
## neg_28_pd 0.2605113905 0.23562384
## neg_29_pd 0.2900940227 0.13571724
## neg_30_pd 0.1999627543 0.12860159
## neg_31_pd 0.1664082361 0.11254461
## neg_32_pd 0.2427354736 0.10707774
## neg_33_pd 0.4302061063 0.16387676
## pos_0_pd 0.0955050485 0.05441567
## pos_1_pd 0.0737250597 0.05808113
## pos_2_pd 0.0988567975 0.05309383
## pos_3_pd 0.0649639253 0.05431523
## pos_4_pd 0.0594982288 0.05440030
## pos_5_pd 0.0162952567 0.05527592
## pos_6_pd 0.0159045526 0.05766612
## pos_7_pd 0.0239061876 0.06042347
## pos_8_pd -0.0279138306 0.05748210
## pos_9_pd -0.0441871036 0.06019791
## pos_10_pd -0.0547338000 0.06391977
## pos_11_pd -0.0667119929 0.05973034
## pos_12_pd -0.0714713887 0.06241043
## pos_13_pd -0.1237184816 0.07071518
## pos_14_pd -0.1086241379 0.07077131
## pos_15_pd -0.1153813424 0.06890663
## pos_16_pd -0.1289392991 0.07121671
## pos_17_pd -0.1219035922 0.07201946
## pos_18_pd -0.1089687946 0.07382395
## pos_19_pd -0.1037184858 0.07137239
## pos_20_pd -0.0984703060 0.07607775
## pos_21_pd -0.1159531705 0.08080575
## pos_22_pd -0.1109416884 0.07949403
## pos_23_pd -0.1089756223 0.08385845
## pos_24_pd -0.1366091424 0.08890092
## pos_25_pd -0.0865538659 0.09865674
## pos_26_pd -0.1013131529 0.09626044
## pos_27_pd -0.1380401111 0.10217791
## pos_28_pd -0.1148876812 0.10526500
## pos_29_pd -0.1172048769 0.11081842
## pos_30_pd -0.0599204594 0.11484068
## pos_31_pd 0.0102632731 0.12847405
## pos_32_pd -0.0522465594 0.12572453
## pos_33_pd -0.0202754733 0.15608705
## pos_34_pd 0.0005228401 0.16061180
## pos_35_pd -0.2424051926 0.13889755
## pos_36_pd -0.2809067482 0.13282853
## pos_37_pd -0.2914015860 0.12427863
## pos_38_pd -0.2751416257 0.12177987
## pos_39_pd -0.2275446476 0.15639983
## s(Time_Period_ID):as.factor(Region)Midwest.1 -0.3846632372 0.05616012
## s(Time_Period_ID):as.factor(Region)Midwest.2 -0.1372031085 0.04459460
## s(Time_Period_ID):as.factor(Region)Midwest.3 0.1799042339 0.04424915
## s(Time_Period_ID):as.factor(Region)Midwest.4 0.4186545216 0.04333833
## s(Time_Period_ID):as.factor(Region)Midwest.5 0.5952791384 0.04193456
## s(Time_Period_ID):as.factor(Region)Midwest.6 0.7917878132 0.04521369
## s(Time_Period_ID):as.factor(Region)Midwest.7 0.9963784224 0.04724867
## s(Time_Period_ID):as.factor(Region)Midwest.8 1.2763364104 0.05983678
## s(Time_Period_ID):as.factor(Region)Midwest.9 1.2269346171 0.06488370
## s(Time_Period_ID):as.factor(Region)Northeast.1 -0.2860818865 0.14516503
## s(Time_Period_ID):as.factor(Region)Northeast.2 -0.1286841648 0.11391202
## s(Time_Period_ID):as.factor(Region)Northeast.3 0.4740726796 0.08577879
## s(Time_Period_ID):as.factor(Region)Northeast.4 0.3977449240 0.08314036
## s(Time_Period_ID):as.factor(Region)Northeast.5 0.5194981681 0.08488821
## s(Time_Period_ID):as.factor(Region)Northeast.6 0.7456277323 0.07770606
## s(Time_Period_ID):as.factor(Region)Northeast.7 1.1508476467 0.08331015
## s(Time_Period_ID):as.factor(Region)Northeast.8 1.6004872852 0.08984903
## s(Time_Period_ID):as.factor(Region)Northeast.9 1.3674676378 0.08316926
## s(Time_Period_ID):as.factor(Region)South.1 -0.2942129097 0.04883124
## s(Time_Period_ID):as.factor(Region)South.2 -0.0560000507 0.03861949
## s(Time_Period_ID):as.factor(Region)South.3 0.2275258950 0.04302954
## s(Time_Period_ID):as.factor(Region)South.4 0.3949428261 0.03819322
## s(Time_Period_ID):as.factor(Region)South.5 0.5317522072 0.03448510
## s(Time_Period_ID):as.factor(Region)South.6 0.6845673191 0.04078241
## s(Time_Period_ID):as.factor(Region)South.7 0.9065685299 0.05033671
## s(Time_Period_ID):as.factor(Region)South.8 1.2327205728 0.06978470
## s(Time_Period_ID):as.factor(Region)South.9 1.1555791005 0.08384363
## s(Time_Period_ID):as.factor(Region)West.1 -0.1895935737 0.06060865
## s(Time_Period_ID):as.factor(Region)West.2 -0.0390095014 0.04713802
## s(Time_Period_ID):as.factor(Region)West.3 0.1604053778 0.04613885
## s(Time_Period_ID):as.factor(Region)West.4 0.3058025724 0.03834480
## s(Time_Period_ID):as.factor(Region)West.5 0.4385296390 0.04128757
## s(Time_Period_ID):as.factor(Region)West.6 0.5605612606 0.04721466
## s(Time_Period_ID):as.factor(Region)West.7 0.6639143157 0.04982420
## s(Time_Period_ID):as.factor(Region)West.8 0.8354902433 0.05914644
## s(Time_Period_ID):as.factor(Region)West.9 0.8222927245 0.06005470
# write.csv(round(sensitivity_anlys_event_study_sd_and_ci, 3), "./Data/event_study_coef_and_ci.csv")
Plot Results
#plot the coefficients for the periods before and after the intervention with 95% CI
plot_event_study_log_smoothed_time <- sensitivity_anlys_event_study_sd_and_ci_log_smoothed_time %>%
mutate(term = rownames(sensitivity_anlys_event_study_sd_and_ci_log_smoothed_time)) %>%
dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
filter(term %in% c(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2),
function(x){paste("neg_", x, "_pd", sep = "")}),
sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_event_study_log_smoothed_time) <- c("term", "estimate", "conf.low", "conf.high")
dwplot(plot_event_study_log_smoothed_time, colour = "black",
vars_order = c(sapply((max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0,
function(x){paste("pos_", x, "_pd", sep = "")}),
sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2),
function(x){paste("neg_", x, "_pd", sep = "")}))) +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black"),
axis.text.x = element_text(angle = 45)) +
geom_vline(aes(xintercept = 0), linetype = "dashed") +
labs(y = "States Excluded", x = "Coefficients and 95% Confidence Intervals",
title = "Coefficient of Pre-Intervention and Post-Intervention Periods") +
scale_color_grey() +
coord_flip() +
geom_hline(yintercept = 33, col = "red", linetype = "dashed")
Plot with Model SD
#compute the full dataset including basis functions
summary_model_log_smoothed <- summary(sensitivity_anlys_event_study_model_log_smoothed_time)
coef_values_log_smoothed <- data.frame(coef_values = coef(sensitivity_anlys_event_study_model_log_smoothed_time),
lb_coef = coef(sensitivity_anlys_event_study_model_log_smoothed_time) -
1.96*summary_model_log_smoothed$se,
ub_coef = coef(sensitivity_anlys_event_study_model_log_smoothed_time) +
1.96*summary_model_log_smoothed$se,
sd_coef = summary_model_log_smoothed$se)
#plot the coefficients for the periods before and after the intervention with 95% CI
plot_event_study_log_smoothed_time_sd_model <- coef_values_log_smoothed %>%
mutate(term = rownames(coef_values_log_smoothed)) %>%
dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
filter(term %in% c(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2),
function(x){paste("neg_", x, "_pd", sep = "")}),
sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_event_study_log_smoothed_time_sd_model) <- c("term", "estimate", "conf.low", "conf.high")
dwplot(plot_event_study_log_smoothed_time_sd_model, colour = "black",
vars_order = c(sapply((max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0,
function(x){paste("pos_", x, "_pd", sep = "")}),
sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2),
function(x){paste("neg_", x, "_pd", sep = "")}))) +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black"),
axis.text.x = element_text(angle = 45)) +
geom_vline(aes(xintercept = 0), linetype = "dashed") +
labs(y = "States Excluded", x = "Coefficients and 95% Confidence Intervals",
title = "Coefficient of Pre-Intervention and Post-Intervention Periods") +
scale_color_grey() +
coord_flip() +
geom_hline(yintercept = 33, col = "red", linetype = "dashed")
Analysis With Only Periods After Treatment
formula_post_tx_log_smoothed_time <- formula(paste("log(prop_dead)~ State +
s(Time_Period_ID, bs = 'cr', by = as.factor(Region)) +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +",
paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_post_tx_model_log_smoothed_time<-gam(formula_post_tx_log_smoothed_time,
data = sensitivity_anlys_event_study_data)
summary(sensitivity_anlys_post_tx_model_log_smoothed_time)
##
## Family: gaussian
## Link function: identity
##
## Formula:
## log(prop_dead) ~ State + s(Time_Period_ID, bs = "cr", by = as.factor(Region)) +
## Naloxone_Pharmacy_Yes_Redefined + Naloxone_Pharmacy_No_Redefined +
## Medical_Marijuana_Redefined + Recreational_Marijuana_Redefined +
## GSL_Redefined + PDMP_Redefined + Medicaid_Expansion_Redefined +
## pos_0_pd + pos_1_pd + pos_2_pd + pos_3_pd + pos_4_pd + pos_5_pd +
## pos_6_pd + pos_7_pd + pos_8_pd + pos_9_pd + pos_10_pd + pos_11_pd +
## pos_12_pd + pos_13_pd + pos_14_pd + pos_15_pd + pos_16_pd +
## pos_17_pd + pos_18_pd + pos_19_pd + pos_20_pd + pos_21_pd +
## pos_22_pd + pos_23_pd + pos_24_pd + pos_25_pd + pos_26_pd +
## pos_27_pd + pos_28_pd + pos_29_pd + pos_30_pd + pos_31_pd +
## pos_32_pd + pos_33_pd + pos_34_pd + pos_35_pd + pos_36_pd +
## pos_37_pd + pos_38_pd + pos_39_pd
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.584292 0.054459 -175.991 < 2e-16 ***
## StateAlaska 0.036666 0.075110 0.488 0.625491
## StateArizona 0.215228 0.067594 3.184 0.001476 **
## StateArkansas -0.548081 0.066435 -8.250 2.94e-16 ***
## StateCalifornia -0.026731 0.075894 -0.352 0.724716
## StateColorado -0.035835 0.073958 -0.485 0.628062
## StateConnecticut 0.222839 0.070167 3.176 0.001518 **
## StateDelaware 0.095876 0.068722 1.395 0.163144
## StateFlorida 0.456984 0.069492 6.576 6.24e-11 ***
## StateGeorgia 0.179243 0.071084 2.522 0.011766 *
## StateHawaii -0.499118 0.073830 -6.760 1.83e-11 ***
## StateIdaho -0.221927 0.067095 -3.308 0.000959 ***
## StateIllinois 0.264387 0.068762 3.845 0.000125 ***
## StateIndiana 0.055252 0.065747 0.840 0.400802
## StateIowa -0.606608 0.066622 -9.105 < 2e-16 ***
## StateKansas -0.220016 0.065338 -3.367 0.000774 ***
## StateKentucky 0.652366 0.066410 9.823 < 2e-16 ***
## StateLouisiana 0.415581 0.066191 6.279 4.23e-10 ***
## StateMaine 0.062938 0.073306 0.859 0.390685
## StateMaryland -1.417519 0.068769 -20.613 < 2e-16 ***
## StateMassachusetts -0.085762 0.066576 -1.288 0.197843
## StateMichigan 0.060031 0.068065 0.882 0.377908
## StateMinnesota -0.642875 0.069185 -9.292 < 2e-16 ***
## StateMississippi -0.144053 0.066275 -2.174 0.029862 *
## StateMissouri 0.201635 0.067794 2.974 0.002974 **
## StateMontana -0.374776 0.070487 -5.317 1.18e-07 ***
## StateNebraska -0.953088 0.067064 -14.212 < 2e-16 ***
## StateNevada 0.503141 0.071408 7.046 2.57e-12 ***
## StateNew Hampshire 0.105971 0.066600 1.591 0.111741
## StateNew Jersey 0.178806 0.068919 2.594 0.009548 **
## StateNew Mexico 0.600453 0.072397 8.294 < 2e-16 ***
## StateNew York -0.130436 0.067618 -1.929 0.053881 .
## StateNorth Carolina 0.288429 0.065582 4.398 1.15e-05 ***
## StateNorth Dakota -1.215260 0.066417 -18.297 < 2e-16 ***
## StateOhio 0.639643 0.071374 8.962 < 2e-16 ***
## StateOklahoma 0.422230 0.065995 6.398 1.98e-10 ***
## StateOregon -0.315309 0.073339 -4.299 1.80e-05 ***
## StatePennsylvania 0.719476 0.069683 10.325 < 2e-16 ***
## StateRhode Island -0.371912 0.069540 -5.348 9.97e-08 ***
## StateSouth Carolina 0.099957 0.066880 1.495 0.135195
## StateSouth Dakota -1.143918 0.067494 -16.949 < 2e-16 ***
## StateTennessee 0.470009 0.064906 7.241 6.44e-13 ***
## StateTexas 0.126538 0.069110 1.831 0.067265 .
## StateUtah -0.043458 0.065711 -0.661 0.508466
## StateVermont -0.206642 0.069102 -2.990 0.002822 **
## StateVirginia 0.056246 0.066538 0.845 0.398035
## StateWashington 0.016780 0.074571 0.225 0.821987
## StateWest Virginia 0.719908 0.066663 10.799 < 2e-16 ***
## StateWisconsin 0.076691 0.066321 1.156 0.247678
## StateWyoming -0.040371 0.065371 -0.618 0.536929
## Naloxone_Pharmacy_Yes_Redefined -0.059310 0.042058 -1.410 0.158653
## Naloxone_Pharmacy_No_Redefined 0.002961 0.038343 0.077 0.938448
## Medical_Marijuana_Redefined 0.202801 0.030716 6.602 5.25e-11 ***
## Recreational_Marijuana_Redefined -0.093791 0.048565 -1.931 0.053606 .
## GSL_Redefined 0.063629 0.031447 2.023 0.043179 *
## PDMP_Redefined -0.173420 0.024533 -7.069 2.19e-12 ***
## Medicaid_Expansion_Redefined 0.086304 0.030150 2.862 0.004250 **
## pos_0_pd -0.023324 0.045506 -0.513 0.608325
## pos_1_pd -0.055506 0.046038 -1.206 0.228103
## pos_2_pd -0.023570 0.046575 -0.506 0.612865
## pos_3_pd -0.062660 0.047171 -1.328 0.184220
## pos_4_pd -0.071229 0.047790 -1.490 0.136271
## pos_5_pd -0.119086 0.048565 -2.452 0.014294 *
## pos_6_pd -0.127267 0.049488 -2.572 0.010197 *
## pos_7_pd -0.128092 0.050341 -2.544 0.011024 *
## pos_8_pd -0.177959 0.051778 -3.437 0.000601 ***
## pos_9_pd -0.203349 0.052920 -3.843 0.000126 ***
## pos_10_pd -0.224738 0.053667 -4.188 2.95e-05 ***
## pos_11_pd -0.232286 0.054842 -4.236 2.39e-05 ***
## pos_12_pd -0.246048 0.056058 -4.389 1.20e-05 ***
## pos_13_pd -0.318017 0.056913 -5.588 2.64e-08 ***
## pos_14_pd -0.306890 0.059028 -5.199 2.22e-07 ***
## pos_15_pd -0.313919 0.060466 -5.192 2.31e-07 ***
## pos_16_pd -0.335444 0.061495 -5.455 5.55e-08 ***
## pos_17_pd -0.333681 0.063816 -5.229 1.90e-07 ***
## pos_18_pd -0.327594 0.065387 -5.010 5.95e-07 ***
## pos_19_pd -0.320472 0.066387 -4.827 1.50e-06 ***
## pos_20_pd -0.328184 0.069238 -4.740 2.30e-06 ***
## pos_21_pd -0.358287 0.072135 -4.967 7.42e-07 ***
## pos_22_pd -0.354073 0.073901 -4.791 1.79e-06 ***
## pos_23_pd -0.364271 0.076024 -4.792 1.79e-06 ***
## pos_24_pd -0.403976 0.080816 -4.999 6.31e-07 ***
## pos_25_pd -0.375638 0.085341 -4.402 1.13e-05 ***
## pos_26_pd -0.388972 0.086291 -4.508 6.96e-06 ***
## pos_27_pd -0.440989 0.087485 -5.041 5.08e-07 ***
## pos_28_pd -0.426885 0.088804 -4.807 1.65e-06 ***
## pos_29_pd -0.443487 0.096615 -4.590 4.72e-06 ***
## pos_30_pd -0.397226 0.099775 -3.981 7.12e-05 ***
## pos_31_pd -0.358305 0.103237 -3.471 0.000531 ***
## pos_32_pd -0.419854 0.113771 -3.690 0.000230 ***
## pos_33_pd -0.451055 0.118929 -3.793 0.000154 ***
## pos_34_pd -0.442611 0.120199 -3.682 0.000238 ***
## pos_35_pd -0.646812 0.139615 -4.633 3.85e-06 ***
## pos_36_pd -0.677019 0.140997 -4.802 1.70e-06 ***
## pos_37_pd -0.675026 0.166873 -4.045 5.44e-05 ***
## pos_38_pd -0.656919 0.222706 -2.950 0.003220 **
## pos_39_pd -0.680624 0.224519 -3.031 0.002467 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(Time_Period_ID):as.factor(Region)Midwest 4.455 5.471 153.62 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)Northeast 8.455 8.915 90.67 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)South 5.852 7.002 117.40 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)West 3.088 3.868 112.48 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.844 Deviance explained = 85.3%
## GCV = 0.089287 Scale est. = 0.083981 n = 2000
Sandwich Estimator
#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_post_tx_log_smoothed_time <-
data.frame(predict(sensitivity_anlys_post_tx_model_log_smoothed_time, type = "lpmatrix"))
#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_post_tx_log_smoothed_time <- coef(sensitivity_anlys_post_tx_model_log_smoothed_time)
sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time <-
compute_sd_and_CI(as.matrix(full_df_w_basis_functions_sensitivity_anlys_post_tx_log_smoothed_time),
log(sensitivity_anlys_event_study_data$prop_dead),
coefficient_values_sensitivity_anlys_post_tx_log_smoothed_time,
p = ncol(full_df_w_basis_functions_sensitivity_anlys_post_tx_log_smoothed_time) - 50)
sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time
## lb_coef coef_values
## (Intercept) -9.6854539768 -9.584291850
## StateAlaska -0.1046639660 0.036665976
## StateArizona 0.1089977014 0.215227642
## StateArkansas -0.6564095521 -0.548081195
## StateCalifornia -0.1545483250 -0.026730935
## StateColorado -0.1541190275 -0.035835468
## StateConnecticut 0.0891506296 0.222839006
## StateDelaware -0.0324643342 0.095876016
## StateFlorida 0.3509994555 0.456983881
## StateGeorgia 0.0815691356 0.179243421
## StateHawaii -0.6267861328 -0.499117982
## StateIdaho -0.3216318260 -0.221926721
## StateIllinois 0.1400446967 0.264386589
## StateIndiana -0.0438355817 0.055252347
## StateIowa -0.7106638951 -0.606607774
## StateKansas -0.3152093450 -0.220016045
## StateKentucky 0.5640805615 0.652366107
## StateLouisiana 0.3200969306 0.415580961
## StateMaine -0.0741560744 0.062938240
## StateMaryland -1.6271647021 -1.417519222
## StateMassachusetts -0.2978866868 -0.085761822
## StateMichigan -0.0328569759 0.060031010
## StateMinnesota -0.7482847354 -0.642874783
## StateMississippi -0.2529389837 -0.144052614
## StateMissouri 0.1111016167 0.201635194
## StateMontana -0.4841245915 -0.374776251
## StateNebraska -1.0504079937 -0.953088399
## StateNevada 0.3948210378 0.503141396
## StateNew Hampshire -0.0070535739 0.105971146
## StateNew Jersey 0.0294406824 0.178806146
## StateNew Mexico 0.4703653251 0.600453346
## StateNew York -0.2486903177 -0.130435518
## StateNorth Carolina 0.2076694369 0.288428714
## StateNorth Dakota -1.3778197767 -1.215260174
## StateOhio 0.5159235266 0.639642699
## StateOklahoma 0.3118844528 0.422229947
## StateOregon -0.4297868703 -0.315309225
## StatePennsylvania 0.6084660641 0.719475961
## StateRhode Island -0.6688200051 -0.371911783
## StateSouth Carolina 0.0018107169 0.099957021
## StateSouth Dakota -1.2718479943 -1.143917518
## StateTennessee 0.3877071260 0.470009368
## StateTexas 0.0119858424 0.126537743
## StateUtah -0.2247810111 -0.043458216
## StateVermont -0.3498881414 -0.206641925
## StateVirginia -0.0376742496 0.056246365
## StateWashington -0.1006345297 0.016780005
## StateWest Virginia 0.5796552871 0.719907762
## StateWisconsin -0.0098912006 0.076691456
## StateWyoming -0.1684715652 -0.040371406
## Naloxone_Pharmacy_Yes_Redefined -0.1232720216 -0.059309662
## Naloxone_Pharmacy_No_Redefined -0.0611427875 0.002961323
## Medical_Marijuana_Redefined 0.1330887661 0.202800700
## Recreational_Marijuana_Redefined -0.1666378312 -0.093790626
## GSL_Redefined 0.0097162405 0.063628690
## PDMP_Redefined -0.2268263907 -0.173420410
## Medicaid_Expansion_Redefined 0.0350389201 0.086304415
## pos_0_pd -0.1024720232 -0.023324068
## pos_1_pd -0.1451126027 -0.055506248
## pos_2_pd -0.1004104047 -0.023570479
## pos_3_pd -0.1414234174 -0.062659755
## pos_4_pd -0.1492366487 -0.071228602
## pos_5_pd -0.1998057945 -0.119086036
## pos_6_pd -0.2139031025 -0.127267389
## pos_7_pd -0.2212403506 -0.128091984
## pos_8_pd -0.2645405128 -0.177959284
## pos_9_pd -0.2965781987 -0.203348513
## pos_10_pd -0.3270500612 -0.224738242
## pos_11_pd -0.3244860166 -0.232285551
## pos_12_pd -0.3455443752 -0.246047943
## pos_13_pd -0.4356205193 -0.318017387
## pos_14_pd -0.4248015800 -0.306890154
## pos_15_pd -0.4261722901 -0.313919283
## pos_16_pd -0.4534278872 -0.335444166
## pos_17_pd -0.4527739444 -0.333680862
## pos_18_pd -0.4491299493 -0.327593795
## pos_19_pd -0.4358931487 -0.320472170
## pos_20_pd -0.4530153148 -0.328184413
## pos_21_pd -0.4934693511 -0.358286616
## pos_22_pd -0.4870884590 -0.354073454
## pos_23_pd -0.5046859006 -0.364270946
## pos_24_pd -0.5539080092 -0.403976112
## pos_25_pd -0.5461140217 -0.375638035
## pos_26_pd -0.5556522361 -0.388971914
## pos_27_pd -0.6207396652 -0.440988642
## pos_28_pd -0.6134503770 -0.426885256
## pos_29_pd -0.6408056504 -0.443487315
## pos_30_pd -0.6024869638 -0.397225581
## pos_31_pd -0.5910035924 -0.358304832
## pos_32_pd -0.6438075396 -0.419853706
## pos_33_pd -0.7387147151 -0.451055372
## pos_34_pd -0.7393531460 -0.442610508
## pos_35_pd -0.8957024262 -0.646811613
## pos_36_pd -0.9116379639 -0.677018978
## pos_37_pd -0.8933535869 -0.675025871
## pos_38_pd -0.8670115452 -0.656919440
## pos_39_pd -0.9658711335 -0.680623994
## s(Time_Period_ID):as.factor(Region)Midwest.1 -0.6326139695 -0.529045004
## s(Time_Period_ID):as.factor(Region)Midwest.2 -0.3390176169 -0.249784199
## s(Time_Period_ID):as.factor(Region)Midwest.3 0.0007546299 0.087068355
## s(Time_Period_ID):as.factor(Region)Midwest.4 0.2573746884 0.343106203
## s(Time_Period_ID):as.factor(Region)Midwest.5 0.4489039132 0.535484239
## s(Time_Period_ID):as.factor(Region)Midwest.6 0.6477021289 0.738911416
## s(Time_Period_ID):as.factor(Region)Midwest.7 0.8641835303 0.954608869
## s(Time_Period_ID):as.factor(Region)Midwest.8 1.1137572711 1.226978851
## s(Time_Period_ID):as.factor(Region)Midwest.9 1.0496931478 1.168645122
## s(Time_Period_ID):as.factor(Region)Northeast.1 -0.8497237979 -0.555935063
## s(Time_Period_ID):as.factor(Region)Northeast.2 -0.5965035114 -0.369120947
## s(Time_Period_ID):as.factor(Region)Northeast.3 0.1420908472 0.314673088
## s(Time_Period_ID):as.factor(Region)Northeast.4 0.0941825739 0.261684737
## s(Time_Period_ID):as.factor(Region)Northeast.5 0.2137588935 0.386082047
## s(Time_Period_ID):as.factor(Region)Northeast.6 0.4862851444 0.644137155
## s(Time_Period_ID):as.factor(Region)Northeast.7 0.8809900634 1.049465437
## s(Time_Period_ID):as.factor(Region)Northeast.8 1.3262754392 1.506472200
## s(Time_Period_ID):as.factor(Region)Northeast.9 1.1173502743 1.280813198
## s(Time_Period_ID):as.factor(Region)South.1 -0.5120365474 -0.429299322
## s(Time_Period_ID):as.factor(Region)South.2 -0.2278641820 -0.156629395
## s(Time_Period_ID):as.factor(Region)South.3 0.0571040728 0.137467348
## s(Time_Period_ID):as.factor(Region)South.4 0.2593436573 0.333216002
## s(Time_Period_ID):as.factor(Region)South.5 0.4287657460 0.492053009
## s(Time_Period_ID):as.factor(Region)South.6 0.5691752517 0.643346729
## s(Time_Period_ID):as.factor(Region)South.7 0.7721608305 0.859875036
## s(Time_Period_ID):as.factor(Region)South.8 1.0412564197 1.162306774
## s(Time_Period_ID):as.factor(Region)South.9 0.9150235656 1.066395234
## s(Time_Period_ID):as.factor(Region)West.1 -0.4481931667 -0.336007136
## s(Time_Period_ID):as.factor(Region)West.2 -0.2307383682 -0.145013221
## s(Time_Period_ID):as.factor(Region)West.3 -0.0138080998 0.072013723
## s(Time_Period_ID):as.factor(Region)West.4 0.1761311647 0.247261807
## s(Time_Period_ID):as.factor(Region)West.5 0.3125934745 0.386821789
## s(Time_Period_ID):as.factor(Region)West.6 0.4208680316 0.508678919
## s(Time_Period_ID):as.factor(Region)West.7 0.5214461873 0.618216906
## s(Time_Period_ID):as.factor(Region)West.8 0.6702804526 0.787663851
## s(Time_Period_ID):as.factor(Region)West.9 0.6624388979 0.774066969
## ub_coef sd_coef
## (Intercept) -9.483129723 0.05161333
## StateAlaska 0.177995918 0.07210711
## StateArizona 0.321457582 0.05419895
## StateArkansas -0.439752837 0.05526957
## StateCalifornia 0.101086456 0.06521295
## StateColorado 0.082448092 0.06034875
## StateConnecticut 0.356527382 0.06820836
## StateDelaware 0.224216366 0.06547977
## StateFlorida 0.562968307 0.05407369
## StateGeorgia 0.276917707 0.04983382
## StateHawaii -0.371449832 0.06513681
## StateIdaho -0.122221617 0.05086995
## StateIllinois 0.388728482 0.06343974
## StateIndiana 0.154340276 0.05055507
## StateIowa -0.502551654 0.05308986
## StateKansas -0.124822744 0.04856801
## StateKentucky 0.740651653 0.04504365
## StateLouisiana 0.511064992 0.04871634
## StateMaine 0.200032554 0.06994608
## StateMaryland -1.207873742 0.10696198
## StateMassachusetts 0.126363042 0.10822697
## StateMichigan 0.152918996 0.04739183
## StateMinnesota -0.537464831 0.05378059
## StateMississippi -0.035166245 0.05555427
## StateMissouri 0.292168772 0.04619060
## StateMontana -0.265427911 0.05578997
## StateNebraska -0.855768805 0.04965285
## StateNevada 0.611461754 0.05526549
## StateNew Hampshire 0.218995866 0.05766567
## StateNew Jersey 0.328171610 0.07620687
## StateNew Mexico 0.730541367 0.06637144
## StateNew York -0.012180719 0.06033408
## StateNorth Carolina 0.369187991 0.04120371
## StateNorth Dakota -1.052700571 0.08293857
## StateOhio 0.763361871 0.06312203
## StateOklahoma 0.532575442 0.05629872
## StateOregon -0.200831581 0.05840696
## StatePennsylvania 0.830485859 0.05663770
## StateRhode Island -0.075003561 0.15148379
## StateSouth Carolina 0.198103326 0.05007465
## StateSouth Dakota -1.015987042 0.06527065
## StateTennessee 0.552311609 0.04199094
## StateTexas 0.241089643 0.05844485
## StateUtah 0.137864579 0.09251163
## StateVermont -0.063395708 0.07308480
## StateVirginia 0.150166979 0.04791868
## StateWashington 0.134194539 0.05990537
## StateWest Virginia 0.860160238 0.07155739
## StateWisconsin 0.163274112 0.04417482
## StateWyoming 0.087728753 0.06535722
## Naloxone_Pharmacy_Yes_Redefined 0.004652698 0.03263386
## Naloxone_Pharmacy_No_Redefined 0.067065434 0.03270618
## Medical_Marijuana_Redefined 0.272512634 0.03556731
## Recreational_Marijuana_Redefined -0.020943422 0.03716694
## GSL_Redefined 0.117541140 0.02750635
## PDMP_Redefined -0.120014429 0.02724795
## Medicaid_Expansion_Redefined 0.137569911 0.02615586
## pos_0_pd 0.055823888 0.04038161
## pos_1_pd 0.034100107 0.04571753
## pos_2_pd 0.053269448 0.03920404
## pos_3_pd 0.016103908 0.04018554
## pos_4_pd 0.006779444 0.03980002
## pos_5_pd -0.038366277 0.04118355
## pos_6_pd -0.040631676 0.04420189
## pos_7_pd -0.034943618 0.04752468
## pos_8_pd -0.091378056 0.04417410
## pos_9_pd -0.110118826 0.04756617
## pos_10_pd -0.122426422 0.05219991
## pos_11_pd -0.140085085 0.04704105
## pos_12_pd -0.146551510 0.05076349
## pos_13_pd -0.200414254 0.06000160
## pos_14_pd -0.188978728 0.06015889
## pos_15_pd -0.201666277 0.05727194
## pos_16_pd -0.217460445 0.06019578
## pos_17_pd -0.214587779 0.06076178
## pos_18_pd -0.206057640 0.06200824
## pos_19_pd -0.205051190 0.05888825
## pos_20_pd -0.203353512 0.06368924
## pos_21_pd -0.223103881 0.06897078
## pos_22_pd -0.221058450 0.06786480
## pos_23_pd -0.223855991 0.07164028
## pos_24_pd -0.254044215 0.07649587
## pos_25_pd -0.205162049 0.08697754
## pos_26_pd -0.222291592 0.08504098
## pos_27_pd -0.261237619 0.09170971
## pos_28_pd -0.240320136 0.09518629
## pos_29_pd -0.246168980 0.10067262
## pos_30_pd -0.191964198 0.10472520
## pos_31_pd -0.125606072 0.11872386
## pos_32_pd -0.195899872 0.11426216
## pos_33_pd -0.163396029 0.14676497
## pos_34_pd -0.145867869 0.15139931
## pos_35_pd -0.397920801 0.12698511
## pos_36_pd -0.442399992 0.11970356
## pos_37_pd -0.456698155 0.11139169
## pos_38_pd -0.446827335 0.10718985
## pos_39_pd -0.395376855 0.14553425
## s(Time_Period_ID):as.factor(Region)Midwest.1 -0.425476039 0.05284131
## s(Time_Period_ID):as.factor(Region)Midwest.2 -0.160550780 0.04552725
## s(Time_Period_ID):as.factor(Region)Midwest.3 0.173382079 0.04403761
## s(Time_Period_ID):as.factor(Region)Midwest.4 0.428837717 0.04374057
## s(Time_Period_ID):as.factor(Region)Midwest.5 0.622064564 0.04417364
## s(Time_Period_ID):as.factor(Region)Midwest.6 0.830120702 0.04653535
## s(Time_Period_ID):as.factor(Region)Midwest.7 1.045034207 0.04613538
## s(Time_Period_ID):as.factor(Region)Midwest.8 1.340200431 0.05776611
## s(Time_Period_ID):as.factor(Region)Midwest.9 1.287597097 0.06068978
## s(Time_Period_ID):as.factor(Region)Northeast.1 -0.262146329 0.14989221
## s(Time_Period_ID):as.factor(Region)Northeast.2 -0.141738382 0.11601151
## s(Time_Period_ID):as.factor(Region)Northeast.3 0.487255330 0.08805216
## s(Time_Period_ID):as.factor(Region)Northeast.4 0.429186901 0.08546029
## s(Time_Period_ID):as.factor(Region)Northeast.5 0.558405201 0.08791998
## s(Time_Period_ID):as.factor(Region)Northeast.6 0.801989165 0.08053674
## s(Time_Period_ID):as.factor(Region)Northeast.7 1.217940811 0.08595682
## s(Time_Period_ID):as.factor(Region)Northeast.8 1.686668961 0.09193712
## s(Time_Period_ID):as.factor(Region)Northeast.9 1.444276122 0.08339945
## s(Time_Period_ID):as.factor(Region)South.1 -0.346562096 0.04221287
## s(Time_Period_ID):as.factor(Region)South.2 -0.085394608 0.03634428
## s(Time_Period_ID):as.factor(Region)South.3 0.217830622 0.04100167
## s(Time_Period_ID):as.factor(Region)South.4 0.407088346 0.03768997
## s(Time_Period_ID):as.factor(Region)South.5 0.555340273 0.03228942
## s(Time_Period_ID):as.factor(Region)South.6 0.717518207 0.03784259
## s(Time_Period_ID):as.factor(Region)South.7 0.947589242 0.04475215
## s(Time_Period_ID):as.factor(Region)South.8 1.283357129 0.06176039
## s(Time_Period_ID):as.factor(Region)South.9 1.217766902 0.07723044
## s(Time_Period_ID):as.factor(Region)West.1 -0.223821106 0.05723777
## s(Time_Period_ID):as.factor(Region)West.2 -0.059288074 0.04373732
## s(Time_Period_ID):as.factor(Region)West.3 0.157835545 0.04378664
## s(Time_Period_ID):as.factor(Region)West.4 0.318392450 0.03629114
## s(Time_Period_ID):as.factor(Region)West.5 0.461050104 0.03787159
## s(Time_Period_ID):as.factor(Region)West.6 0.596489806 0.04480147
## s(Time_Period_ID):as.factor(Region)West.7 0.714987624 0.04937282
## s(Time_Period_ID):as.factor(Region)West.8 0.905047249 0.05988949
## s(Time_Period_ID):as.factor(Region)West.9 0.885695041 0.05695310
Plot Results
#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx_log_smoothed_time <- sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time %>%
mutate(term = rownames(sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time)) %>%
dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
filter(term %in% c(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_post_tx_log_smoothed_time) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx_log_smoothed_time$num_states <- sapply(plot_post_tx_log_smoothed_time$term,
function(x){sum(sensitivity_anlys_event_study_data[,x])})
dwplot(plot_post_tx_log_smoothed_time, colour = "black",
vars_order = c(sapply(((max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0),
function(x){paste("pos_", x, "_pd", sep = "")}))) +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black"),
axis.text.x = element_text(angle = 45, size = 4)) +
geom_vline(aes(xintercept = 0), linetype = "dashed") +
labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals",
title = "Coefficient of Post-Intervention Periods") +
scale_color_grey() +
coord_flip()
# geom_vline(aes(xintercept = coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"]), linetype = "dashed", color = "red") +
# geom_text(aes(label = paste("Coefficient Estimate: ", coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"]), y = 12,
# x = coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"] + 0.1), color = "red")
# geom_text(aes(label = num_states, x = .1, y = 40:1), size = 2)
Attributable Deaths
date_data <- sensitivity_anlys_event_study_data[, c("Time_Period_ID", "Time_Period_Start")]
date_data <- date_data[!duplicated(date_data),]
attr_deaths_est_log_smoothed_time_post_tx <- attr_death_compute(sensitivity_anlys_event_study_data,
sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time)
attr_deaths_est_log_smoothed_time_post_tx <- merge(attr_deaths_est_log_smoothed_time_post_tx, date_data,
by.x = "Time_Period", by.y = "Time_Period_ID")
ggplot(attr_deaths_est_log_smoothed_time_post_tx, aes(x = Time_Period_Start)) +
# geom_point(aes(y = attr_deaths)) +
geom_line(aes(y = attr_deaths, linetype = "Estimate")) +
# geom_point(aes(y = attr_deaths_lb)) +
geom_line(aes(y = attr_deaths_lb, linetype = "95% CI")) +
# geom_point(aes(y = attr_deaths_ub)) +
geom_line(aes(y = attr_deaths_ub, linetype = "95% CI")) +
labs(x = "Date", y = "Attributable Deaths",
title = "Estimated Number of Attributable Deaths Using Semi-Dynamic Model",
linetype = "") +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black")) +
scale_linetype_manual(values = c("dashed", "solid"))
Model With Semi Dynamic Regression
coef_semi_dynamic <- data.frame(matrix(NA, nrow = 40, ncol = 4))
for(time in 0:39){
subset_data <- sensitivity_anlys_event_study_data %>%
filter(get(paste("pos_", time, "_pd", sep = "")) == 1 |
Time_Period_Start <= Intervention_First_Date)
formula_semi_dynamic <- formula(paste("log(prop_dead)~ State +
s(Time_Period_ID, bs = 'cr', by = as.factor(Region)) +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +",
paste("pos_", time, "_pd", sep = "")))
#run the gam model
semi_dynamic_model<-gam(formula_semi_dynamic, data = subset_data)
summary_semi_dynamic_model <- summary(semi_dynamic_model)
sd_semi_dynamic_model <- summary_semi_dynamic_model$se[paste("pos_", time, "_pd", sep = "")]
coef_value <- coef(semi_dynamic_model)[paste("pos_", time, "_pd", sep = "")]
coef_semi_dynamic[time + 1,] <- c(time, coef_value, coef_value - 1.96*sd_semi_dynamic_model, coef_value + 1.96*sd_semi_dynamic_model)
}
colnames(coef_semi_dynamic) <- c("time_after_tx", "estimate", "lb", "ub")
ggplot(coef_semi_dynamic, aes(y = estimate, x = time_after_tx)) +
geom_pointrange(aes(ymin = lb, ymax = ub), fatten = 1)
Analysis With Only Periods After Treatment with Model SD
summary_model_log_smoothed_post_tx <- summary(sensitivity_anlys_post_tx_model_log_smoothed_time)
coef_values_log_smoothed_post_tx <- data.frame(coef_values = coef(sensitivity_anlys_post_tx_model_log_smoothed_time),
lb_coef = coef(sensitivity_anlys_post_tx_model_log_smoothed_time) -
1.96*summary_model_log_smoothed_post_tx$se,
ub_coef = coef(sensitivity_anlys_post_tx_model_log_smoothed_time) +
1.96*summary_model_log_smoothed_post_tx$se,
sd_coef = summary_model_log_smoothed_post_tx$se)
Plot Results
#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx_log_smoothed_time_post_tx <- coef_values_log_smoothed_post_tx %>%
mutate(term = rownames(coef_values_log_smoothed_post_tx)) %>%
dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
filter(term %in% c(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_post_tx_log_smoothed_time_post_tx) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx_log_smoothed_time_post_tx$num_states <- sapply(plot_post_tx_log_smoothed_time_post_tx$term,
function(x){sum(sensitivity_anlys_event_study_data[,x])})
dwplot(plot_post_tx_log_smoothed_time_post_tx, colour = "black",
vars_order = c(sapply(((max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0),
function(x){paste("pos_", x, "_pd", sep = "")}))) +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black"),
axis.text.x = element_text(angle = 45, size = 4)) +
geom_vline(aes(xintercept = 0), linetype = "dashed") +
labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals",
title = "Coefficient of Pre-Intervention and Post-Intervention Periods") +
scale_color_grey() +
coord_flip() +
geom_vline(aes(xintercept = coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"]), linetype = "dashed", color = "red") +
geom_text(aes(label = paste("Coefficient Estimate: ", coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"]), y = 12,
x = coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"] + 0.1), color = "red")
# geom_text(aes(label = num_states, x = .1, y = 40:1), size = 2)
Analysis With Linear Periods After Treatment
#use this function to compute the cumulative sum, but resets the sum if the variable was 0
compute_cumsum = function(x){
cs = cumsum(x)
cs - cummax((x == 0) * cs)
}
sensitivity_anlys_event_study_data_lin_post_tx <- sensitivity_anlys_event_study_data %>%
arrange(State, Time_Period_ID) %>%
group_by(State) %>%
mutate(sum_tx_periods = pos_0_pd + pos_1_pd + pos_2_pd + pos_3_pd +
pos_4_pd + pos_5_pd + pos_6_pd + pos_7_pd + pos_8_pd + pos_9_pd +
pos_10_pd + pos_11_pd + pos_12_pd + pos_13_pd + pos_14_pd +
pos_15_pd + pos_16_pd + pos_17_pd + pos_18_pd + pos_19_pd +
pos_20_pd + pos_21_pd + pos_22_pd + pos_23_pd + pos_24_pd +
pos_25_pd + pos_26_pd + pos_27_pd + pos_28_pd + pos_29_pd +
pos_30_pd + pos_31_pd + pos_32_pd + pos_33_pd + pos_34_pd +
pos_35_pd + pos_36_pd + pos_37_pd + pos_38_pd + pos_39_pd,
time_after_tx = cumsum(sum_tx_periods),
num_pd_w_tx = compute_cumsum(Intervention_Redefined ),
num_pd_w_naloxone_yes = compute_cumsum(Naloxone_Pharmacy_Yes_Redefined),
num_pd_w_naloxone_no = compute_cumsum(Naloxone_Pharmacy_No_Redefined),
num_pd_w_med_marijuana = compute_cumsum(Medical_Marijuana_Redefined),
num_pd_w_rec_marijuana = compute_cumsum(Recreational_Marijuana_Redefined),
num_pd_w_gsl = compute_cumsum(GSL_Redefined),
num_pd_w_pdmp = compute_cumsum(PDMP_Redefined),
num_pd_w_medicaid = compute_cumsum(Medicaid_Expansion_Redefined),
lag_num_pd_w_tx = lag(num_pd_w_tx)) #lag so that intercept = effect when tx first occurs
#fill in a 0 for the NAs so we keep all the data and at most this will be 0
sensitivity_anlys_event_study_data_lin_post_tx$lag_num_pd_w_tx[is.na(sensitivity_anlys_event_study_data_lin_post_tx$lag_num_pd_w_tx)] <- 0
#run the gam model
sensitivity_anlys_lin_post_tx_model_log_smoothed_time<-gam(log(prop_dead)~ State +
s(Time_Period_ID, bs = 'cr', by = as.factor(Region)) +
num_pd_w_naloxone_yes +
num_pd_w_naloxone_no +
num_pd_w_med_marijuana +
num_pd_w_rec_marijuana +
num_pd_w_gsl +
num_pd_w_pdmp +
num_pd_w_medicaid +
Intervention_Redefined +
lag_num_pd_w_tx,
data = sensitivity_anlys_event_study_data_lin_post_tx)
summary(sensitivity_anlys_lin_post_tx_model_log_smoothed_time)
##
## Family: gaussian
## Link function: identity
##
## Formula:
## log(prop_dead) ~ State + s(Time_Period_ID, bs = "cr", by = as.factor(Region)) +
## num_pd_w_naloxone_yes + num_pd_w_naloxone_no + num_pd_w_med_marijuana +
## num_pd_w_rec_marijuana + num_pd_w_gsl + num_pd_w_pdmp + num_pd_w_medicaid +
## Intervention_Redefined + lag_num_pd_w_tx
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.8183490 0.0556256 -176.508 < 2e-16 ***
## StateAlaska 0.4171746 0.0802721 5.197 2.24e-07 ***
## StateArizona 0.3760830 0.0670104 5.612 2.29e-08 ***
## StateArkansas -0.4059470 0.0678565 -5.982 2.62e-09 ***
## StateCalifornia 0.1638949 0.0827625 1.980 0.047812 *
## StateColorado 0.3024756 0.0756626 3.998 6.64e-05 ***
## StateConnecticut 0.3454200 0.0727701 4.747 2.22e-06 ***
## StateDelaware 0.3161505 0.0688666 4.591 4.70e-06 ***
## StateFlorida 0.5664793 0.0701076 8.080 1.13e-15 ***
## StateGeorgia 0.3153556 0.0718656 4.388 1.21e-05 ***
## StateHawaii -0.3147575 0.0821161 -3.833 0.000131 ***
## StateIdaho -0.3507383 0.0699840 -5.012 5.89e-07 ***
## StateIllinois 0.2758364 0.0729175 3.783 0.000160 ***
## StateIndiana -0.1025759 0.0686310 -1.495 0.135183
## StateIowa -0.6002178 0.0666147 -9.010 < 2e-16 ***
## StateKansas -0.1640845 0.0658173 -2.493 0.012749 *
## StateKentucky 0.5163621 0.0690509 7.478 1.14e-13 ***
## StateLouisiana 0.4502306 0.0662037 6.801 1.39e-11 ***
## StateMaine 0.3826328 0.0789499 4.847 1.36e-06 ***
## StateMaryland -1.2575835 0.0707303 -17.780 < 2e-16 ***
## StateMassachusetts -0.1576709 0.0687445 -2.294 0.021922 *
## StateMichigan 0.0580381 0.0706337 0.822 0.411362
## StateMinnesota -0.4026034 0.0705033 -5.710 1.30e-08 ***
## StateMississippi -0.1421124 0.0662557 -2.145 0.032086 *
## StateMissouri 0.4574842 0.0700174 6.534 8.19e-11 ***
## StateMontana -0.0003051 0.0725785 -0.004 0.996646
## StateNebraska -0.8175986 0.0677976 -12.059 < 2e-16 ***
## StateNevada 0.6546011 0.0775381 8.442 < 2e-16 ***
## StateNew Hampshire 0.3207231 0.0679253 4.722 2.51e-06 ***
## StateNew Jersey 0.3458793 0.0693044 4.991 6.56e-07 ***
## StateNew Mexico 0.7922907 0.0784424 10.100 < 2e-16 ***
## StateNew York -0.1990437 0.0699730 -2.845 0.004494 **
## StateNorth Carolina 0.3142558 0.0659779 4.763 2.05e-06 ***
## StateNorth Dakota -1.1760400 0.0663083 -17.736 < 2e-16 ***
## StateOhio 0.6677233 0.0704338 9.480 < 2e-16 ***
## StateOklahoma 0.3057100 0.0686792 4.451 9.03e-06 ***
## StateOregon 0.1541645 0.0775496 1.988 0.046960 *
## StatePennsylvania 0.6210185 0.0718327 8.645 < 2e-16 ***
## StateRhode Island -0.2827495 0.0723100 -3.910 9.54e-05 ***
## StateSouth Carolina 0.1340333 0.0668806 2.004 0.045203 *
## StateSouth Dakota -1.0307736 0.0683303 -15.085 < 2e-16 ***
## StateTennessee 0.4235722 0.0655056 6.466 1.27e-10 ***
## StateTexas -0.0059759 0.0713798 -0.084 0.933288
## StateUtah -0.1801834 0.0690426 -2.610 0.009132 **
## StateVermont 0.0681485 0.0695052 0.980 0.326972
## StateVirginia -0.0067563 0.0672381 -0.100 0.919971
## StateWashington 0.3781016 0.0768966 4.917 9.54e-07 ***
## StateWest Virginia 0.5864998 0.0697456 8.409 < 2e-16 ***
## StateWisconsin 0.1798570 0.0673732 2.670 0.007659 **
## StateWyoming -0.1055152 0.0657774 -1.604 0.108851
## num_pd_w_naloxone_yes -0.0274867 0.0064854 -4.238 2.36e-05 ***
## num_pd_w_naloxone_no -0.0118751 0.0036375 -3.265 0.001115 **
## num_pd_w_med_marijuana -0.0077139 0.0021669 -3.560 0.000380 ***
## num_pd_w_rec_marijuana -0.0231385 0.0080380 -2.879 0.004038 **
## num_pd_w_gsl 0.0148938 0.0037555 3.966 7.58e-05 ***
## num_pd_w_pdmp 0.0104664 0.0022420 4.668 3.25e-06 ***
## num_pd_w_medicaid 0.0223990 0.0042380 5.285 1.40e-07 ***
## Intervention_Redefined -0.0609092 0.0244971 -2.486 0.012989 *
## lag_num_pd_w_tx -0.0140202 0.0018155 -7.722 1.83e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(Time_Period_ID):as.factor(Region)Midwest 4.781 5.844 95.38 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)Northeast 8.525 8.934 61.79 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)South 5.798 6.947 63.35 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)West 4.177 5.173 40.06 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.843 Deviance explained = 84.9%
## GCV = 0.087961 Scale est. = 0.084342 n = 2000
plot(sensitivity_anlys_lin_post_tx_model_log_smoothed_time, pages = 1)
Sandwich Estimator
#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_lin_post_tx_log_smoothed_time <-
data.frame(predict(sensitivity_anlys_lin_post_tx_model_log_smoothed_time, type = "lpmatrix"))
#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_lin_post_tx_log_smoothed_time <- coef(sensitivity_anlys_lin_post_tx_model_log_smoothed_time)
sensitivity_anlys_lin_post_tx_sd_and_ci_log_smoothed_time <-
compute_sd_and_CI(as.matrix(full_df_w_basis_functions_sensitivity_anlys_lin_post_tx_log_smoothed_time),
log(sensitivity_anlys_event_study_data$prop_dead),
coefficient_values_sensitivity_anlys_lin_post_tx_log_smoothed_time,
p = ncol(full_df_w_basis_functions_sensitivity_anlys_lin_post_tx_log_smoothed_time) - 50)
round(sensitivity_anlys_lin_post_tx_sd_and_ci_log_smoothed_time, 3)
## lb_coef coef_values ub_coef
## (Intercept) -10.059 -9.818 -9.578
## StateAlaska 0.079 0.417 0.755
## StateArizona 0.128 0.376 0.624
## StateArkansas -0.722 -0.406 -0.090
## StateCalifornia -0.187 0.164 0.515
## StateColorado -0.007 0.302 0.612
## StateConnecticut -0.016 0.345 0.707
## StateDelaware 0.036 0.316 0.596
## StateFlorida 0.286 0.566 0.846
## StateGeorgia 0.033 0.315 0.598
## StateHawaii -0.676 -0.315 0.046
## StateIdaho -0.621 -0.351 -0.080
## StateIllinois -0.014 0.276 0.566
## StateIndiana -0.453 -0.103 0.248
## StateIowa -0.905 -0.600 -0.295
## StateKansas -0.439 -0.164 0.111
## StateKentucky 0.216 0.516 0.816
## StateLouisiana 0.164 0.450 0.736
## StateMaine 0.008 0.383 0.757
## StateMaryland -1.600 -1.258 -0.916
## StateMassachusetts -0.657 -0.158 0.341
## StateMichigan -0.251 0.058 0.367
## StateMinnesota -0.707 -0.403 -0.099
## StateMississippi -0.426 -0.142 0.142
## StateMissouri 0.180 0.457 0.735
## StateMontana -0.287 0.000 0.287
## StateNebraska -1.115 -0.818 -0.520
## StateNevada 0.332 0.655 0.977
## StateNew Hampshire -0.004 0.321 0.645
## StateNew Jersey 0.036 0.346 0.656
## StateNew Mexico 0.465 0.792 1.120
## StateNew York -0.538 -0.199 0.140
## StateNorth Carolina 0.054 0.314 0.575
## StateNorth Dakota -1.496 -1.176 -0.856
## StateOhio 0.339 0.668 0.997
## StateOklahoma 0.002 0.306 0.609
## StateOregon -0.176 0.154 0.485
## StatePennsylvania 0.286 0.621 0.956
## StateRhode Island -0.835 -0.283 0.270
## StateSouth Carolina -0.161 0.134 0.429
## StateSouth Dakota -1.370 -1.031 -0.691
## StateTennessee 0.146 0.424 0.701
## StateTexas -0.287 -0.006 0.275
## StateUtah -0.505 -0.180 0.144
## StateVermont -0.246 0.068 0.383
## StateVirginia -0.271 -0.007 0.257
## StateWashington 0.061 0.378 0.695
## StateWest Virginia 0.251 0.586 0.922
## StateWisconsin -0.111 0.180 0.471
## StateWyoming -0.378 -0.106 0.167
## num_pd_w_naloxone_yes -0.067 -0.027 0.012
## num_pd_w_naloxone_no -0.028 -0.012 0.004
## num_pd_w_med_marijuana -0.020 -0.008 0.005
## num_pd_w_rec_marijuana -0.070 -0.023 0.024
## num_pd_w_gsl -0.007 0.015 0.036
## num_pd_w_pdmp 0.000 0.010 0.021
## num_pd_w_medicaid -0.005 0.022 0.050
## Intervention_Redefined -0.161 -0.061 0.039
## lag_num_pd_w_tx -0.023 -0.014 -0.005
## s(Time_Period_ID):as.factor(Region)Midwest.1 -0.659 -0.455 -0.251
## s(Time_Period_ID):as.factor(Region)Midwest.2 -0.365 -0.181 0.003
## s(Time_Period_ID):as.factor(Region)Midwest.3 -0.021 0.121 0.262
## s(Time_Period_ID):as.factor(Region)Midwest.4 0.191 0.323 0.456
## s(Time_Period_ID):as.factor(Region)Midwest.5 0.248 0.454 0.660
## s(Time_Period_ID):as.factor(Region)Midwest.6 0.452 0.621 0.790
## s(Time_Period_ID):as.factor(Region)Midwest.7 0.612 0.833 1.053
## s(Time_Period_ID):as.factor(Region)Midwest.8 0.677 1.095 1.512
## s(Time_Period_ID):as.factor(Region)Midwest.9 0.413 1.050 1.686
## s(Time_Period_ID):as.factor(Region)Northeast.1 -0.884 -0.521 -0.157
## s(Time_Period_ID):as.factor(Region)Northeast.2 -0.633 -0.352 -0.071
## s(Time_Period_ID):as.factor(Region)Northeast.3 0.077 0.319 0.562
## s(Time_Period_ID):as.factor(Region)Northeast.4 0.005 0.221 0.438
## s(Time_Period_ID):as.factor(Region)Northeast.5 0.048 0.363 0.678
## s(Time_Period_ID):as.factor(Region)Northeast.6 0.337 0.629 0.921
## s(Time_Period_ID):as.factor(Region)Northeast.7 0.669 0.997 1.324
## s(Time_Period_ID):as.factor(Region)Northeast.8 0.790 1.421 2.053
## s(Time_Period_ID):as.factor(Region)Northeast.9 0.193 1.196 2.199
## s(Time_Period_ID):as.factor(Region)South.1 -0.507 -0.328 -0.150
## s(Time_Period_ID):as.factor(Region)South.2 -0.235 -0.086 0.063
## s(Time_Period_ID):as.factor(Region)South.3 0.019 0.141 0.262
## s(Time_Period_ID):as.factor(Region)South.4 0.176 0.279 0.382
## s(Time_Period_ID):as.factor(Region)South.5 0.221 0.381 0.541
## s(Time_Period_ID):as.factor(Region)South.6 0.333 0.494 0.655
## s(Time_Period_ID):as.factor(Region)South.7 0.492 0.698 0.903
## s(Time_Period_ID):as.factor(Region)South.8 0.624 0.995 1.365
## s(Time_Period_ID):as.factor(Region)South.9 0.384 0.945 1.506
## s(Time_Period_ID):as.factor(Region)West.1 -0.441 -0.272 -0.103
## s(Time_Period_ID):as.factor(Region)West.2 -0.222 -0.075 0.072
## s(Time_Period_ID):as.factor(Region)West.3 0.013 0.130 0.248
## s(Time_Period_ID):as.factor(Region)West.4 0.181 0.291 0.401
## s(Time_Period_ID):as.factor(Region)West.5 0.208 0.391 0.575
## s(Time_Period_ID):as.factor(Region)West.6 0.273 0.459 0.644
## s(Time_Period_ID):as.factor(Region)West.7 0.294 0.515 0.735
## s(Time_Period_ID):as.factor(Region)West.8 0.318 0.657 0.995
## s(Time_Period_ID):as.factor(Region)West.9 0.139 0.656 1.173
## sd_coef
## (Intercept) 0.123
## StateAlaska 0.172
## StateArizona 0.127
## StateArkansas 0.161
## StateCalifornia 0.179
## StateColorado 0.158
## StateConnecticut 0.184
## StateDelaware 0.143
## StateFlorida 0.143
## StateGeorgia 0.144
## StateHawaii 0.184
## StateIdaho 0.138
## StateIllinois 0.148
## StateIndiana 0.179
## StateIowa 0.156
## StateKansas 0.140
## StateKentucky 0.153
## StateLouisiana 0.146
## StateMaine 0.191
## StateMaryland 0.174
## StateMassachusetts 0.255
## StateMichigan 0.157
## StateMinnesota 0.155
## StateMississippi 0.145
## StateMissouri 0.142
## StateMontana 0.146
## StateNebraska 0.152
## StateNevada 0.165
## StateNew Hampshire 0.166
## StateNew Jersey 0.158
## StateNew Mexico 0.167
## StateNew York 0.173
## StateNorth Carolina 0.133
## StateNorth Dakota 0.163
## StateOhio 0.168
## StateOklahoma 0.155
## StateOregon 0.169
## StatePennsylvania 0.171
## StateRhode Island 0.282
## StateSouth Carolina 0.150
## StateSouth Dakota 0.173
## StateTennessee 0.142
## StateTexas 0.143
## StateUtah 0.166
## StateVermont 0.161
## StateVirginia 0.135
## StateWashington 0.162
## StateWest Virginia 0.171
## StateWisconsin 0.148
## StateWyoming 0.139
## num_pd_w_naloxone_yes 0.020
## num_pd_w_naloxone_no 0.008
## num_pd_w_med_marijuana 0.006
## num_pd_w_rec_marijuana 0.024
## num_pd_w_gsl 0.011
## num_pd_w_pdmp 0.005
## num_pd_w_medicaid 0.014
## Intervention_Redefined 0.051
## lag_num_pd_w_tx 0.005
## s(Time_Period_ID):as.factor(Region)Midwest.1 0.104
## s(Time_Period_ID):as.factor(Region)Midwest.2 0.094
## s(Time_Period_ID):as.factor(Region)Midwest.3 0.072
## s(Time_Period_ID):as.factor(Region)Midwest.4 0.068
## s(Time_Period_ID):as.factor(Region)Midwest.5 0.105
## s(Time_Period_ID):as.factor(Region)Midwest.6 0.086
## s(Time_Period_ID):as.factor(Region)Midwest.7 0.113
## s(Time_Period_ID):as.factor(Region)Midwest.8 0.213
## s(Time_Period_ID):as.factor(Region)Midwest.9 0.325
## s(Time_Period_ID):as.factor(Region)Northeast.1 0.185
## s(Time_Period_ID):as.factor(Region)Northeast.2 0.143
## s(Time_Period_ID):as.factor(Region)Northeast.3 0.124
## s(Time_Period_ID):as.factor(Region)Northeast.4 0.110
## s(Time_Period_ID):as.factor(Region)Northeast.5 0.161
## s(Time_Period_ID):as.factor(Region)Northeast.6 0.149
## s(Time_Period_ID):as.factor(Region)Northeast.7 0.167
## s(Time_Period_ID):as.factor(Region)Northeast.8 0.322
## s(Time_Period_ID):as.factor(Region)Northeast.9 0.512
## s(Time_Period_ID):as.factor(Region)South.1 0.091
## s(Time_Period_ID):as.factor(Region)South.2 0.076
## s(Time_Period_ID):as.factor(Region)South.3 0.062
## s(Time_Period_ID):as.factor(Region)South.4 0.052
## s(Time_Period_ID):as.factor(Region)South.5 0.082
## s(Time_Period_ID):as.factor(Region)South.6 0.082
## s(Time_Period_ID):as.factor(Region)South.7 0.105
## s(Time_Period_ID):as.factor(Region)South.8 0.189
## s(Time_Period_ID):as.factor(Region)South.9 0.286
## s(Time_Period_ID):as.factor(Region)West.1 0.086
## s(Time_Period_ID):as.factor(Region)West.2 0.075
## s(Time_Period_ID):as.factor(Region)West.3 0.060
## s(Time_Period_ID):as.factor(Region)West.4 0.056
## s(Time_Period_ID):as.factor(Region)West.5 0.094
## s(Time_Period_ID):as.factor(Region)West.6 0.095
## s(Time_Period_ID):as.factor(Region)West.7 0.113
## s(Time_Period_ID):as.factor(Region)West.8 0.173
## s(Time_Period_ID):as.factor(Region)West.9 0.264
Attributable Deaths
date_data <- sensitivity_anlys_event_study_data_lin_post_tx[, c("Time_Period_ID", "Time_Period_Start")]
date_data <- date_data[!duplicated(date_data),]
attr_deaths_est_log_smoothed_time_lin_post <- attr_death_compute(sensitivity_anlys_event_study_data_lin_post_tx,
sensitivity_anlys_lin_post_tx_sd_and_ci_log_smoothed_time,
post_tx_model = FALSE, tx_name = "num_pd_w_tx")
attr_deaths_est_log_smoothed_time_lin_post <- merge(attr_deaths_est_log_smoothed_time_lin_post, date_data,
by.x = "Time_Period", by.y = "Time_Period_ID")
ggplot(attr_deaths_est_log_smoothed_time_lin_post, aes(x = Time_Period_Start)) +
# geom_point(aes(y = attr_deaths)) +
geom_line(aes(y = attr_deaths, linetype = "Estimate")) +
# geom_point(aes(y = attr_deaths_lb)) +
geom_line(aes(y = attr_deaths_lb, linetype = "95% CI")) +
# geom_point(aes(y = attr_deaths_ub)) +
geom_line(aes(y = attr_deaths_ub, linetype = "95% CI")) +
labs(x = "Date", y = "Attributable Deaths",
title = "Estimated Number of Attributable Deaths Using Smoothed Time Effects,
Log Probability of Drug Overdose Death, Linear Policy Effects",
linetype = "") +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black")) +
scale_linetype_manual(values = c("dashed", "solid"))
Analysis With Only Periods After Treatment Subset Periods
formula_post_tx_log_smoothed_time <- formula(paste("log(prop_dead)~ State +
s(Time_Period_ID, bs = 'cr', by = as.factor(Region)) +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +",
paste(sapply(0:(29 -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
data_subset <- sensitivity_anlys_event_study_data[sensitivity_anlys_event_study_data$Time_Period_ID <= 29,]
sensitivity_anlys_post_tx_model_log_smoothed_time_subset<-gam(formula_post_tx_log_smoothed_time,
data = data_subset)
summary(sensitivity_anlys_post_tx_model_log_smoothed_time_subset)
##
## Family: gaussian
## Link function: identity
##
## Formula:
## log(prop_dead) ~ State + s(Time_Period_ID, bs = "cr", by = as.factor(Region)) +
## Naloxone_Pharmacy_Yes_Redefined + Naloxone_Pharmacy_No_Redefined +
## Medical_Marijuana_Redefined + Recreational_Marijuana_Redefined +
## GSL_Redefined + PDMP_Redefined + Medicaid_Expansion_Redefined +
## pos_0_pd + pos_1_pd + pos_2_pd + pos_3_pd + pos_4_pd + pos_5_pd +
## pos_6_pd + pos_7_pd + pos_8_pd + pos_9_pd + pos_10_pd + pos_11_pd +
## pos_12_pd + pos_13_pd + pos_14_pd + pos_15_pd + pos_16_pd +
## pos_17_pd + pos_18_pd + pos_19_pd + pos_20_pd + pos_21_pd +
## pos_22_pd + pos_23_pd + pos_24_pd + pos_25_pd + pos_26_pd +
## pos_27_pd + pos_28_pd
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.862725 0.059773 -165.004 < 2e-16 ***
## StateAlaska 0.212414 0.090977 2.335 0.019699 *
## StateArizona 0.362667 0.079584 4.557 5.66e-06 ***
## StateArkansas -0.530538 0.079466 -6.676 3.57e-11 ***
## StateCalifornia 0.193632 0.095742 2.022 0.043328 *
## StateColorado 0.090068 0.089227 1.009 0.312949
## StateConnecticut 0.314760 0.088485 3.557 0.000388 ***
## StateDelaware 0.083216 0.080454 1.034 0.301169
## StateFlorida 0.537193 0.083477 6.435 1.71e-10 ***
## StateGeorgia 0.224657 0.085947 2.614 0.009051 **
## StateHawaii -0.347263 0.089344 -3.887 0.000107 ***
## StateIdaho -0.110161 0.079916 -1.378 0.168290
## StateIllinois 0.458008 0.084604 5.414 7.30e-08 ***
## StateIndiana -0.004068 0.078860 -0.052 0.958866
## StateIowa -0.611468 0.078991 -7.741 1.92e-14 ***
## StateKansas -0.170941 0.078231 -2.185 0.029054 *
## StateKentucky 0.727742 0.079503 9.154 < 2e-16 ***
## StateLouisiana 0.446253 0.079310 5.627 2.23e-08 ***
## StateMaine 0.010420 0.088712 0.117 0.906514
## StateMaryland -1.670260 0.083298 -20.052 < 2e-16 ***
## StateMassachusetts -0.239084 0.079192 -3.019 0.002584 **
## StateMichigan 0.082081 0.080795 1.016 0.309849
## StateMinnesota -0.602405 0.084229 -7.152 1.40e-12 ***
## StateMississippi -0.005186 0.079223 -0.065 0.947818
## StateMissouri 0.205192 0.080431 2.551 0.010846 *
## StateMontana -0.245674 0.085185 -2.884 0.003989 **
## StateNebraska -0.924887 0.079776 -11.594 < 2e-16 ***
## StateNevada 0.702655 0.087215 8.057 1.71e-15 ***
## StateNew Hampshire -0.004402 0.079592 -0.055 0.955904
## StateNew Jersey 0.178997 0.081931 2.185 0.029080 *
## StateNew Mexico 0.891722 0.095342 9.353 < 2e-16 ***
## StateNew York -0.024124 0.084196 -0.287 0.774524
## StateNorth Carolina 0.320215 0.078953 4.056 5.28e-05 ***
## StateNorth Dakota -1.280818 0.078923 -16.229 < 2e-16 ***
## StateOhio 0.577535 0.085178 6.780 1.79e-11 ***
## StateOklahoma 0.571781 0.079148 7.224 8.40e-13 ***
## StateOregon -0.179475 0.089597 -2.003 0.045362 *
## StatePennsylvania 0.759541 0.083695 9.075 < 2e-16 ***
## StateRhode Island -0.520918 0.083581 -6.232 6.13e-10 ***
## StateSouth Carolina 0.159320 0.079254 2.010 0.044604 *
## StateSouth Dakota -1.147427 0.079829 -14.374 < 2e-16 ***
## StateTennessee 0.466473 0.078090 5.974 2.97e-09 ***
## StateTexas 0.282478 0.082866 3.409 0.000672 ***
## StateUtah -0.095084 0.079262 -1.200 0.230497
## StateVermont -0.175811 0.083479 -2.106 0.035383 *
## StateVirginia 0.065475 0.080026 0.818 0.413407
## StateWashington 0.212332 0.090920 2.335 0.019670 *
## StateWest Virginia 0.732124 0.079582 9.200 < 2e-16 ***
## StateWisconsin 0.037389 0.079858 0.468 0.639723
## StateWyoming 0.019764 0.078216 0.253 0.800547
## Naloxone_Pharmacy_Yes_Redefined -0.284390 0.082934 -3.429 0.000624 ***
## Naloxone_Pharmacy_No_Redefined -0.086503 0.057196 -1.512 0.130668
## Medical_Marijuana_Redefined 0.184293 0.042111 4.376 1.30e-05 ***
## Recreational_Marijuana_Redefined -0.109736 0.145171 -0.756 0.449838
## GSL_Redefined 0.045889 0.051826 0.885 0.376081
## PDMP_Redefined -0.200586 0.028819 -6.960 5.28e-12 ***
## Medicaid_Expansion_Redefined -0.017545 0.054275 -0.323 0.746552
## pos_0_pd -0.013641 0.049650 -0.275 0.783552
## pos_1_pd -0.071942 0.050652 -1.420 0.155746
## pos_2_pd -0.025125 0.051288 -0.490 0.624297
## pos_3_pd -0.071828 0.053549 -1.341 0.180032
## pos_4_pd -0.071123 0.054886 -1.296 0.195252
## pos_5_pd -0.106578 0.055901 -1.907 0.056792 .
## pos_6_pd -0.134623 0.057990 -2.321 0.020409 *
## pos_7_pd -0.126421 0.059190 -2.136 0.032870 *
## pos_8_pd -0.166563 0.060121 -2.770 0.005674 **
## pos_9_pd -0.208846 0.063200 -3.305 0.000976 ***
## pos_10_pd -0.244293 0.066207 -3.690 0.000233 ***
## pos_11_pd -0.229367 0.067742 -3.386 0.000730 ***
## pos_12_pd -0.257327 0.069765 -3.689 0.000235 ***
## pos_13_pd -0.365723 0.074808 -4.889 1.14e-06 ***
## pos_14_pd -0.350234 0.079677 -4.396 1.19e-05 ***
## pos_15_pd -0.264112 0.080681 -3.274 0.001089 **
## pos_16_pd -0.296031 0.081807 -3.619 0.000307 ***
## pos_17_pd -0.311984 0.083093 -3.755 0.000181 ***
## pos_18_pd -0.307130 0.091697 -3.349 0.000832 ***
## pos_19_pd -0.281092 0.095203 -2.953 0.003206 **
## pos_20_pd -0.285711 0.098787 -2.892 0.003887 **
## pos_21_pd -0.328115 0.110391 -2.972 0.003008 **
## pos_22_pd -0.345412 0.116534 -2.964 0.003090 **
## pos_23_pd -0.393804 0.118868 -3.313 0.000948 ***
## pos_24_pd -0.529046 0.137904 -3.836 0.000131 ***
## pos_25_pd -0.546115 0.139495 -3.915 9.49e-05 ***
## pos_26_pd -0.522451 0.166403 -3.140 0.001728 **
## pos_27_pd -0.437444 0.225048 -1.944 0.052130 .
## pos_28_pd -0.244808 0.228925 -1.069 0.285088
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(Time_Period_ID):as.factor(Region)Midwest 2.429 3.029 206.58 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)Northeast 7.447 8.397 64.25 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)South 2.857 3.558 179.50 <2e-16 ***
## s(Time_Period_ID):as.factor(Region)West 2.302 2.878 127.07 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.816 Deviance explained = 82.9%
## GCV = 0.094699 Scale est. = 0.0881 n = 1450
Sandwich Estimator
#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_post_tx_log_smoothed_time_subset <-
data.frame(predict(sensitivity_anlys_post_tx_model_log_smoothed_time_subset, type = "lpmatrix"))
#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_post_tx_log_smoothed_time_subset <- coef(sensitivity_anlys_post_tx_model_log_smoothed_time_subset)
sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time_subset <-
compute_sd_and_CI(as.matrix(full_df_w_basis_functions_sensitivity_anlys_post_tx_log_smoothed_time_subset),
log(data_subset$prop_dead),
coefficient_values_sensitivity_anlys_post_tx_log_smoothed_time_subset,
p = ncol(full_df_w_basis_functions_sensitivity_anlys_post_tx_log_smoothed_time_subset) - 50)
sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time_subset
## lb_coef coef_values
## (Intercept) -9.973242764 -9.862725482
## StateAlaska 0.030029695 0.212414446
## StateArizona 0.235473910 0.362667104
## StateArkansas -0.669357583 -0.530537691
## StateCalifornia 0.017783771 0.193631956
## StateColorado -0.065292619 0.090068337
## StateConnecticut 0.135999538 0.314759770
## StateDelaware -0.063735645 0.083215545
## StateFlorida 0.410868395 0.537193243
## StateGeorgia 0.100095122 0.224657142
## StateHawaii -0.507826084 -0.347262824
## StateIdaho -0.234424109 -0.110161183
## StateIllinois 0.325912939 0.458007875
## StateIndiana -0.120693237 -0.004068115
## StateIowa -0.741281924 -0.611468419
## StateKansas -0.288051105 -0.170941069
## StateKentucky 0.616746282 0.727741657
## StateLouisiana 0.321049907 0.446253201
## StateMaine -0.177528437 0.010419932
## StateMaryland -1.868203240 -1.670260245
## StateMassachusetts -0.508779128 -0.239083840
## StateMichigan -0.031501236 0.082080926
## StateMinnesota -0.740527224 -0.602404704
## StateMississippi -0.123799504 -0.005185847
## StateMissouri 0.096518983 0.205191613
## StateMontana -0.385556467 -0.245673894
## StateNebraska -1.043938298 -0.924886581
## StateNevada 0.566172640 0.702654874
## StateNew Hampshire -0.148090598 -0.004401802
## StateNew Jersey -0.011379492 0.178997370
## StateNew Mexico 0.706962026 0.891721593
## StateNew York -0.176639545 -0.024123712
## StateNorth Carolina 0.217134430 0.320214716
## StateNorth Dakota -1.491629505 -1.280818174
## StateOhio 0.425900211 0.577535139
## StateOklahoma 0.460835760 0.571781079
## StateOregon -0.334250654 -0.179475237
## StatePennsylvania 0.625509542 0.759541236
## StateRhode Island -0.908033445 -0.520917738
## StateSouth Carolina 0.038306724 0.159320137
## StateSouth Dakota -1.307649853 -1.147426537
## StateTennessee 0.360071601 0.466472779
## StateTexas 0.154841933 0.282477733
## StateUtah -0.297147646 -0.095083851
## StateVermont -0.357220539 -0.175811301
## StateVirginia -0.054840847 0.065474678
## StateWashington 0.057295704 0.212331764
## StateWest Virginia 0.551757191 0.732123709
## StateWisconsin -0.071393881 0.037388815
## StateWyoming -0.132491707 0.019764436
## Naloxone_Pharmacy_Yes_Redefined -0.402616193 -0.284390220
## Naloxone_Pharmacy_No_Redefined -0.205794848 -0.086502721
## Medical_Marijuana_Redefined 0.079208577 0.184292505
## Recreational_Marijuana_Redefined -0.278228478 -0.109735670
## GSL_Redefined -0.054615051 0.045888641
## PDMP_Redefined -0.257222183 -0.200585732
## Medicaid_Expansion_Redefined -0.107491848 -0.017544585
## pos_0_pd -0.099925615 -0.013641245
## pos_1_pd -0.167291650 -0.071941536
## pos_2_pd -0.105556368 -0.025124924
## pos_3_pd -0.154038586 -0.071827871
## pos_4_pd -0.150512944 -0.071123103
## pos_5_pd -0.193500070 -0.106577884
## pos_6_pd -0.231858556 -0.134622844
## pos_7_pd -0.231502747 -0.126420780
## pos_8_pd -0.262459251 -0.166562838
## pos_9_pd -0.320178960 -0.208846260
## pos_10_pd -0.369801838 -0.244293238
## pos_11_pd -0.338478739 -0.229366928
## pos_12_pd -0.379824201 -0.257327000
## pos_13_pd -0.531192866 -0.365723111
## pos_14_pd -0.524590515 -0.350234166
## pos_15_pd -0.391752279 -0.264111549
## pos_16_pd -0.437541338 -0.296030852
## pos_17_pd -0.458735161 -0.311983614
## pos_18_pd -0.471358331 -0.307129986
## pos_19_pd -0.438420814 -0.281091994
## pos_20_pd -0.463836535 -0.285710584
## pos_21_pd -0.562884149 -0.328114602
## pos_22_pd -0.613816528 -0.345411706
## pos_23_pd -0.648454982 -0.393804343
## pos_24_pd -0.745318376 -0.529045906
## pos_25_pd -0.767274756 -0.546115201
## pos_26_pd -0.798404490 -0.522450793
## pos_27_pd -0.664142924 -0.437444010
## pos_28_pd -0.461949852 -0.244808392
## s(Time_Period_ID):as.factor(Region)Midwest.1 -0.534848240 -0.435880992
## s(Time_Period_ID):as.factor(Region)Midwest.2 -0.326382928 -0.237608613
## s(Time_Period_ID):as.factor(Region)Midwest.3 -0.090492660 0.010782212
## s(Time_Period_ID):as.factor(Region)Midwest.4 0.137266609 0.233869614
## s(Time_Period_ID):as.factor(Region)Midwest.5 0.333757553 0.439242815
## s(Time_Period_ID):as.factor(Region)Midwest.6 0.531352147 0.621167429
## s(Time_Period_ID):as.factor(Region)Midwest.7 0.663382014 0.770061218
## s(Time_Period_ID):as.factor(Region)Midwest.8 0.849363529 0.963521101
## s(Time_Period_ID):as.factor(Region)Midwest.9 0.843682581 0.960091243
## s(Time_Period_ID):as.factor(Region)Northeast.1 -0.741889256 -0.459073113
## s(Time_Period_ID):as.factor(Region)Northeast.2 -0.527521719 -0.291441706
## s(Time_Period_ID):as.factor(Region)Northeast.3 -0.311926440 -0.054312038
## s(Time_Period_ID):as.factor(Region)Northeast.4 0.310402416 0.499558659
## s(Time_Period_ID):as.factor(Region)Northeast.5 0.390052304 0.585604773
## s(Time_Period_ID):as.factor(Region)Northeast.6 0.290344230 0.504138247
## s(Time_Period_ID):as.factor(Region)Northeast.7 0.443993825 0.639736699
## s(Time_Period_ID):as.factor(Region)Northeast.8 0.716344533 0.917205803
## s(Time_Period_ID):as.factor(Region)Northeast.9 0.870381499 1.091103894
## s(Time_Period_ID):as.factor(Region)South.1 -0.467345778 -0.381056024
## s(Time_Period_ID):as.factor(Region)South.2 -0.241859170 -0.167637612
## s(Time_Period_ID):as.factor(Region)South.3 -0.007180722 0.069613509
## s(Time_Period_ID):as.factor(Region)South.4 0.187031499 0.265394961
## s(Time_Period_ID):as.factor(Region)South.5 0.354470163 0.430160759
## s(Time_Period_ID):as.factor(Region)South.6 0.484595451 0.569532471
## s(Time_Period_ID):as.factor(Region)South.7 0.600966960 0.685448745
## s(Time_Period_ID):as.factor(Region)South.8 0.749582832 0.851122838
## s(Time_Period_ID):as.factor(Region)South.9 0.705110292 0.834017294
## s(Time_Period_ID):as.factor(Region)West.1 -0.422746695 -0.304616044
## s(Time_Period_ID):as.factor(Region)West.2 -0.242255731 -0.156595834
## s(Time_Period_ID):as.factor(Region)West.3 -0.070184131 0.015901091
## s(Time_Period_ID):as.factor(Region)West.4 0.089618625 0.168392108
## s(Time_Period_ID):as.factor(Region)West.5 0.236401125 0.313119188
## s(Time_Period_ID):as.factor(Region)West.6 0.363290257 0.443694096
## s(Time_Period_ID):as.factor(Region)West.7 0.460635234 0.550484292
## s(Time_Period_ID):as.factor(Region)West.8 0.574372960 0.689663400
## s(Time_Period_ID):as.factor(Region)West.9 0.514004682 0.687288177
## ub_coef sd_coef
## (Intercept) -9.752208201 0.05638637
## StateAlaska 0.394799197 0.09305344
## StateArizona 0.489860298 0.06489449
## StateArkansas -0.391717800 0.07082648
## StateCalifornia 0.369480141 0.08971846
## StateColorado 0.245429293 0.07926579
## StateConnecticut 0.493520002 0.09120420
## StateDelaware 0.230166734 0.07497510
## StateFlorida 0.663518090 0.06445145
## StateGeorgia 0.349219162 0.06355205
## StateHawaii -0.186699564 0.08192003
## StateIdaho 0.014101743 0.06339945
## StateIllinois 0.590102812 0.06739538
## StateIndiana 0.112557007 0.05950261
## StateIowa -0.481654913 0.06623138
## StateKansas -0.053831034 0.05975002
## StateKentucky 0.838737032 0.05663029
## StateLouisiana 0.571456495 0.06387923
## StateMaine 0.198368301 0.09589202
## StateMaryland -1.472317250 0.10099132
## StateMassachusetts 0.030611449 0.13759964
## StateMichigan 0.195663087 0.05795008
## StateMinnesota -0.464282184 0.07047067
## StateMississippi 0.113427809 0.06051717
## StateMissouri 0.313864243 0.05544522
## StateMontana -0.105791320 0.07136866
## StateNebraska -0.805834864 0.06074067
## StateNevada 0.839137108 0.06963379
## StateNew Hampshire 0.139286993 0.07331061
## StateNew Jersey 0.369374232 0.09713105
## StateNew Mexico 1.076481160 0.09426509
## StateNew York 0.128392122 0.07781420
## StateNorth Carolina 0.423295003 0.05259198
## StateNorth Dakota -1.070006842 0.10755680
## StateOhio 0.729170068 0.07736476
## StateOklahoma 0.682726397 0.05660475
## StateOregon -0.024699820 0.07896705
## StatePennsylvania 0.893572930 0.06838352
## StateRhode Island -0.133802031 0.19750801
## StateSouth Carolina 0.280333550 0.06174154
## StateSouth Dakota -0.987203221 0.08174659
## StateTennessee 0.572873956 0.05428632
## StateTexas 0.410113533 0.06512031
## StateUtah 0.106979945 0.10309377
## StateVermont 0.005597938 0.09255573
## StateVirginia 0.185790202 0.06138547
## StateWashington 0.367367825 0.07910003
## StateWest Virginia 0.912490227 0.09202373
## StateWisconsin 0.146171511 0.05550138
## StateWyoming 0.172020579 0.07768171
## Naloxone_Pharmacy_Yes_Redefined -0.166164247 0.06031937
## Naloxone_Pharmacy_No_Redefined 0.032789407 0.06086333
## Medical_Marijuana_Redefined 0.289376432 0.05361425
## Recreational_Marijuana_Redefined 0.058757138 0.08596572
## GSL_Redefined 0.146392333 0.05127739
## PDMP_Redefined -0.143949281 0.02889615
## Medicaid_Expansion_Redefined 0.072402679 0.04589146
## pos_0_pd 0.072643126 0.04402264
## pos_1_pd 0.023408579 0.04864802
## pos_2_pd 0.055306520 0.04103645
## pos_3_pd 0.010382844 0.04194424
## pos_4_pd 0.008266737 0.04050502
## pos_5_pd -0.019655698 0.04434805
## pos_6_pd -0.037387133 0.04961006
## pos_7_pd -0.021338814 0.05361325
## pos_8_pd -0.070666424 0.04892674
## pos_9_pd -0.097513561 0.05680240
## pos_10_pd -0.118784638 0.06403500
## pos_11_pd -0.120255117 0.05566929
## pos_12_pd -0.134829799 0.06249857
## pos_13_pd -0.200253355 0.08442334
## pos_14_pd -0.175877817 0.08895732
## pos_15_pd -0.136470819 0.06512282
## pos_16_pd -0.154520366 0.07219923
## pos_17_pd -0.165232067 0.07487324
## pos_18_pd -0.142901642 0.08378997
## pos_19_pd -0.123763173 0.08026981
## pos_20_pd -0.107584633 0.09088059
## pos_21_pd -0.093345054 0.11978038
## pos_22_pd -0.077006884 0.13694124
## pos_23_pd -0.139153705 0.12992380
## pos_24_pd -0.312773436 0.11034310
## pos_25_pd -0.324955646 0.11283651
## pos_26_pd -0.246497096 0.14079270
## pos_27_pd -0.210745096 0.11566271
## pos_28_pd -0.027666932 0.11078646
## s(Time_Period_ID):as.factor(Region)Midwest.1 -0.336913744 0.05049349
## s(Time_Period_ID):as.factor(Region)Midwest.2 -0.148834299 0.04529302
## s(Time_Period_ID):as.factor(Region)Midwest.3 0.112057084 0.05167085
## s(Time_Period_ID):as.factor(Region)Midwest.4 0.330472619 0.04928725
## s(Time_Period_ID):as.factor(Region)Midwest.5 0.544728077 0.05381901
## s(Time_Period_ID):as.factor(Region)Midwest.6 0.710982710 0.04582412
## s(Time_Period_ID):as.factor(Region)Midwest.7 0.876740422 0.05442817
## s(Time_Period_ID):as.factor(Region)Midwest.8 1.077678673 0.05824366
## s(Time_Period_ID):as.factor(Region)Midwest.9 1.076499906 0.05939217
## s(Time_Period_ID):as.factor(Region)Northeast.1 -0.176256970 0.14429395
## s(Time_Period_ID):as.factor(Region)Northeast.2 -0.055361694 0.12044899
## s(Time_Period_ID):as.factor(Region)Northeast.3 0.203302365 0.13143592
## s(Time_Period_ID):as.factor(Region)Northeast.4 0.688714902 0.09650829
## s(Time_Period_ID):as.factor(Region)Northeast.5 0.781157241 0.09977167
## s(Time_Period_ID):as.factor(Region)Northeast.6 0.717932264 0.10907858
## s(Time_Period_ID):as.factor(Region)Northeast.7 0.835479573 0.09986881
## s(Time_Period_ID):as.factor(Region)Northeast.8 1.118067073 0.10248024
## s(Time_Period_ID):as.factor(Region)Northeast.9 1.311826289 0.11261347
## s(Time_Period_ID):as.factor(Region)South.1 -0.294766271 0.04402538
## s(Time_Period_ID):as.factor(Region)South.2 -0.093416054 0.03786814
## s(Time_Period_ID):as.factor(Region)South.3 0.146407740 0.03918073
## s(Time_Period_ID):as.factor(Region)South.4 0.343758422 0.03998136
## s(Time_Period_ID):as.factor(Region)South.5 0.505851355 0.03861765
## s(Time_Period_ID):as.factor(Region)South.6 0.654469492 0.04333521
## s(Time_Period_ID):as.factor(Region)South.7 0.769930529 0.04310295
## s(Time_Period_ID):as.factor(Region)South.8 0.952662844 0.05180613
## s(Time_Period_ID):as.factor(Region)South.9 0.962924296 0.06576888
## s(Time_Period_ID):as.factor(Region)West.1 -0.186485393 0.06027074
## s(Time_Period_ID):as.factor(Region)West.2 -0.070935938 0.04370403
## s(Time_Period_ID):as.factor(Region)West.3 0.101986312 0.04392103
## s(Time_Period_ID):as.factor(Region)West.4 0.247165591 0.04019055
## s(Time_Period_ID):as.factor(Region)West.5 0.389837252 0.03914187
## s(Time_Period_ID):as.factor(Region)West.6 0.524097935 0.04102237
## s(Time_Period_ID):as.factor(Region)West.7 0.640333349 0.04584136
## s(Time_Period_ID):as.factor(Region)West.8 0.804953841 0.05882165
## s(Time_Period_ID):as.factor(Region)West.9 0.860571672 0.08840995
Plot Results
#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx_log_smoothed_time_subset <- sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time_subset %>%
mutate(term = rownames(sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time_subset)) %>%
dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
filter(term %in% c(sapply(0:(max(data_subset$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_post_tx_log_smoothed_time_subset) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx_log_smoothed_time_subset$num_states <- sapply(plot_post_tx_log_smoothed_time_subset$term,
function(x){sum(sensitivity_anlys_event_study_data[,x])})
plot_post_tx_data <- merge(plot_post_tx_log_smoothed_time, plot_post_tx_log_smoothed_time_subset,
by = "term", all.x = TRUE)
plot_post_tx_data$term <- factor(plot_post_tx_data$term,
levels = sapply(0:39, function(x){paste("pos_", x, "_pd", sep = "")}))
ggplot(plot_post_tx_data, aes(x = term)) +
geom_point(plot_post_tx_data, mapping = aes(y = estimate.y, color = "subset data")) +
geom_pointrange(plot_post_tx_data,
mapping = aes(x = term, y = estimate.y, ymin = conf.low.y, ymax = conf.high.y, color = "subset data"),
fatten = 1, alpha = .5) +
geom_point(plot_post_tx_data, mapping = aes(y = estimate.x, color = "full data")) +
geom_pointrange(plot_post_tx_data,
mapping = aes(x = term, y = estimate.x, ymin = conf.low.x, ymax = conf.high.x, color = "full data"),
fatten = 1, alpha = .5) +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black"),
axis.text.x = element_text(angle = 45, size = 4),
legend.position = "bottom") +
geom_hline(aes(yintercept = 0), linetype = "dashed") +
labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals",
title = "Coefficient of Pre-Intervention and Post-Intervention Periods",
color = "Full Data or Subset Times")
# geom_vline(aes(xintercept = coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"]), linetype = "dashed", color = "red") +
# geom_text(aes(label = paste("Coefficient Estimate: ", coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"]), y = 12,
# x = coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"] + 0.1), color = "red")
# geom_text(aes(label = num_states, x = .1, y = 40:1), size = 2)
OLS Model Main Analysis With Fixed Time Effects Interacted with Region With Log Proportion
#compute the proportion of people who died from drug overdose
main_analysis_data$prop_dead <- main_analysis_data$imputed_deaths/main_analysis_data$population
#fit an OLS with smoothed time effects
main_analysis_model_log_fixed_time<-lm(log(prop_dead)~ State +
factor(Time_Period_ID) +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +
Intervention_Redefined ,
data = main_analysis_data)
summary(main_analysis_model_log_fixed_time)
##
## Call:
## lm(formula = log(prop_dead) ~ State + factor(Time_Period_ID) +
## Naloxone_Pharmacy_Yes_Redefined + Naloxone_Pharmacy_No_Redefined +
## Medical_Marijuana_Redefined + Recreational_Marijuana_Redefined +
## GSL_Redefined + PDMP_Redefined + Medicaid_Expansion_Redefined +
## Intervention_Redefined, data = main_analysis_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.16662 -0.14440 0.01557 0.16375 1.01553
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.070e+01 6.658e-02 -160.743 < 2e-16 ***
## StateAlaska 1.164e-01 7.781e-02 1.495 0.13498
## StateArizona 2.490e-01 7.153e-02 3.481 0.00051 ***
## StateArkansas -5.008e-01 7.062e-02 -7.092 1.86e-12 ***
## StateCalifornia -2.310e-01 7.771e-02 -2.973 0.00299 **
## StateColorado 2.546e-03 7.741e-02 0.033 0.97377
## StateConnecticut 1.765e-01 7.464e-02 2.365 0.01812 *
## StateDelaware 1.793e-01 7.180e-02 2.497 0.01262 *
## StateFlorida 2.975e-01 7.066e-02 4.210 2.67e-05 ***
## StateGeorgia 9.257e-04 7.067e-02 0.013 0.98955
## StateHawaii -4.627e-01 7.666e-02 -6.036 1.90e-09 ***
## StateIdaho -1.269e-01 7.068e-02 -1.795 0.07284 .
## StateIllinois 1.306e-01 7.168e-02 1.822 0.06859 .
## StateIndiana 8.123e-02 7.029e-02 1.156 0.24798
## StateIowa -6.772e-01 7.046e-02 -9.611 < 2e-16 ***
## StateKansas -2.301e-01 6.994e-02 -3.290 0.00102 **
## StateKentucky 6.993e-01 7.077e-02 9.882 < 2e-16 ***
## StateLouisiana 3.399e-01 6.985e-02 4.867 1.23e-06 ***
## StateMaine 1.993e-02 7.758e-02 0.257 0.79726
## StateMaryland -1.540e+00 7.152e-02 -21.525 < 2e-16 ***
## StateMassachusetts -9.582e-02 7.113e-02 -1.347 0.17814
## StateMichigan -3.275e-02 7.216e-02 -0.454 0.64994
## StateMinnesota -7.108e-01 7.336e-02 -9.689 < 2e-16 ***
## StateMississippi -4.987e-02 6.990e-02 -0.713 0.47565
## StateMissouri 1.644e-01 7.223e-02 2.276 0.02294 *
## StateMontana -5.026e-01 7.387e-02 -6.803 1.37e-11 ***
## StateNebraska -8.789e-01 7.103e-02 -12.373 < 2e-16 ***
## StateNevada 4.032e-01 7.528e-02 5.357 9.50e-08 ***
## StateNew Hampshire 1.198e-01 7.095e-02 1.689 0.09144 .
## StateNew Jersey 4.021e-02 7.161e-02 0.562 0.57445
## StateNew Mexico 5.692e-01 7.626e-02 7.464 1.27e-13 ***
## StateNew York -1.778e-01 7.217e-02 -2.464 0.01384 *
## StateNorth Carolina 2.328e-01 6.973e-02 3.338 0.00086 ***
## StateNorth Dakota -1.151e+00 7.034e-02 -16.366 < 2e-16 ***
## StateOhio 4.362e-01 7.083e-02 6.158 8.97e-10 ***
## StateOklahoma 4.533e-01 7.036e-02 6.443 1.48e-10 ***
## StateOregon -3.275e-01 7.715e-02 -4.246 2.28e-05 ***
## StatePennsylvania 5.452e-01 7.074e-02 7.707 2.05e-14 ***
## StateRhode Island -3.432e-01 7.307e-02 -4.697 2.83e-06 ***
## StateSouth Carolina 2.059e-01 7.028e-02 2.930 0.00343 **
## StateSouth Dakota -1.028e+00 7.069e-02 -14.538 < 2e-16 ***
## StateTennessee 4.674e-01 6.955e-02 6.721 2.38e-11 ***
## StateTexas -2.100e-02 7.064e-02 -0.297 0.76627
## StateUtah -1.021e-01 6.996e-02 -1.460 0.14450
## StateVermont -2.267e-01 7.319e-02 -3.098 0.00198 **
## StateVirginia -3.502e-02 6.986e-02 -0.501 0.61623
## StateWashington 2.417e-03 7.834e-02 0.031 0.97539
## StateWest Virginia 7.778e-01 7.074e-02 10.995 < 2e-16 ***
## StateWisconsin 5.883e-03 7.000e-02 0.084 0.93303
## StateWyoming -2.170e-02 6.991e-02 -0.310 0.75634
## factor(Time_Period_ID)2 -4.194e-03 6.211e-02 -0.068 0.94618
## factor(Time_Period_ID)3 1.132e-01 6.213e-02 1.822 0.06861 .
## factor(Time_Period_ID)4 1.623e-01 6.217e-02 2.610 0.00911 **
## factor(Time_Period_ID)5 3.199e-01 6.219e-02 5.143 2.98e-07 ***
## factor(Time_Period_ID)6 3.397e-01 6.226e-02 5.455 5.52e-08 ***
## factor(Time_Period_ID)7 4.779e-01 6.229e-02 7.673 2.66e-14 ***
## factor(Time_Period_ID)8 4.621e-01 6.233e-02 7.413 1.85e-13 ***
## factor(Time_Period_ID)9 5.468e-01 6.242e-02 8.760 < 2e-16 ***
## factor(Time_Period_ID)10 5.440e-01 6.258e-02 8.693 < 2e-16 ***
## factor(Time_Period_ID)11 6.607e-01 6.270e-02 10.537 < 2e-16 ***
## factor(Time_Period_ID)12 6.757e-01 6.302e-02 10.722 < 2e-16 ***
## factor(Time_Period_ID)13 8.393e-01 6.322e-02 13.277 < 2e-16 ***
## factor(Time_Period_ID)14 8.891e-01 6.348e-02 14.005 < 2e-16 ***
## factor(Time_Period_ID)15 9.345e-01 6.348e-02 14.721 < 2e-16 ***
## factor(Time_Period_ID)16 9.466e-01 6.376e-02 14.846 < 2e-16 ***
## factor(Time_Period_ID)17 1.029e+00 6.432e-02 16.005 < 2e-16 ***
## factor(Time_Period_ID)18 1.030e+00 6.461e-02 15.947 < 2e-16 ***
## factor(Time_Period_ID)19 1.016e+00 6.485e-02 15.669 < 2e-16 ***
## factor(Time_Period_ID)20 1.021e+00 6.525e-02 15.645 < 2e-16 ***
## factor(Time_Period_ID)21 1.057e+00 6.559e-02 16.113 < 2e-16 ***
## factor(Time_Period_ID)22 1.024e+00 6.607e-02 15.499 < 2e-16 ***
## factor(Time_Period_ID)23 1.169e+00 6.633e-02 17.629 < 2e-16 ***
## factor(Time_Period_ID)24 1.162e+00 6.708e-02 17.325 < 2e-16 ***
## factor(Time_Period_ID)25 1.157e+00 6.731e-02 17.185 < 2e-16 ***
## factor(Time_Period_ID)26 1.160e+00 6.769e-02 17.135 < 2e-16 ***
## factor(Time_Period_ID)27 1.255e+00 6.836e-02 18.360 < 2e-16 ***
## factor(Time_Period_ID)28 1.224e+00 6.905e-02 17.727 < 2e-16 ***
## factor(Time_Period_ID)29 1.275e+00 6.993e-02 18.237 < 2e-16 ***
## factor(Time_Period_ID)30 1.283e+00 7.118e-02 18.019 < 2e-16 ***
## factor(Time_Period_ID)31 1.385e+00 7.188e-02 19.262 < 2e-16 ***
## factor(Time_Period_ID)32 1.414e+00 7.509e-02 18.834 < 2e-16 ***
## factor(Time_Period_ID)33 1.554e+00 7.663e-02 20.286 < 2e-16 ***
## factor(Time_Period_ID)34 1.583e+00 7.971e-02 19.857 < 2e-16 ***
## factor(Time_Period_ID)35 1.635e+00 8.065e-02 20.279 < 2e-16 ***
## factor(Time_Period_ID)36 1.643e+00 8.215e-02 20.005 < 2e-16 ***
## factor(Time_Period_ID)37 1.621e+00 8.220e-02 19.724 < 2e-16 ***
## factor(Time_Period_ID)38 1.593e+00 8.257e-02 19.298 < 2e-16 ***
## factor(Time_Period_ID)39 1.624e+00 8.282e-02 19.611 < 2e-16 ***
## factor(Time_Period_ID)40 1.683e+00 8.292e-02 20.302 < 2e-16 ***
## Naloxone_Pharmacy_Yes_Redefined -5.662e-02 4.607e-02 -1.229 0.21924
## Naloxone_Pharmacy_No_Redefined 3.659e-02 3.916e-02 0.934 0.35022
## Medical_Marijuana_Redefined 2.778e-01 3.084e-02 9.006 < 2e-16 ***
## Recreational_Marijuana_Redefined -2.535e-01 4.663e-02 -5.437 6.12e-08 ***
## GSL_Redefined 4.494e-02 3.270e-02 1.374 0.16950
## PDMP_Redefined -1.514e-01 2.593e-02 -5.839 6.15e-09 ***
## Medicaid_Expansion_Redefined 9.274e-02 3.195e-02 2.903 0.00374 **
## Intervention_Redefined -2.813e-02 2.536e-02 -1.109 0.26742
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3105 on 1903 degrees of freedom
## Multiple R-squared: 0.8292, Adjusted R-squared: 0.8206
## F-statistic: 96.25 on 96 and 1903 DF, p-value: < 2.2e-16
#examine fitted values
summary(fitted(main_analysis_model_log_fixed_time))
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -12.246 -10.224 -9.743 -9.796 -9.334 -8.061
hist(fitted(main_analysis_model_log_fixed_time))
par(mfrow = c(2,2))
plot(main_analysis_model_log_fixed_time)
Coefficients and 95% CI
#compute the full dataset including basis functions
full_df_w_basis_functions_log_fixed_time <- model.matrix(main_analysis_model_log_fixed_time)
#estimate the 95% CI and SD
coefficient_values_log_fixed_time <- coef(main_analysis_model_log_fixed_time)
#type = "response" to get the estimated probabilities
main_analysis_sd_and_ci_log_fixed_time <- compute_sd_and_CI(full_df_w_basis_functions_log_fixed_time, log(main_analysis_data$prop_dead),
coefficient_values_log_fixed_time,
p = ncol(full_df_w_basis_functions_log_fixed_time) - 50)
main_analysis_sd_and_ci_log_fixed_time
## lb_coef coef_values ub_coef
## (Intercept) -10.850377438 -1.070190e+01 -10.55342460
## StateAlaska -0.024222451 1.163638e-01 0.25695010
## StateArizona 0.123163944 2.490087e-01 0.37485344
## StateArkansas -0.615183054 -5.008129e-01 -0.38644280
## StateCalifornia -0.366193094 -2.310104e-01 -0.09582777
## StateColorado -0.120489769 2.545702e-03 0.12558117
## StateConnecticut 0.053335063 1.765235e-01 0.29971188
## StateDelaware 0.060279724 1.792553e-01 0.29823083
## StateFlorida 0.193187574 2.975306e-01 0.40187353
## StateGeorgia -0.083673688 9.256537e-04 0.08552500
## StateHawaii -0.581782815 -4.626592e-01 -0.34353560
## StateIdaho -0.223147224 -1.268582e-01 -0.03056909
## StateIllinois 0.016246056 1.306158e-01 0.24498551
## StateIndiana -0.032281040 8.122898e-02 0.19473900
## StateIowa -0.776424451 -6.771603e-01 -0.57789615
## StateKansas -0.323691489 -2.300818e-01 -0.13647210
## StateKentucky 0.614299989 6.993124e-01 0.78432472
## StateLouisiana 0.249464265 3.399497e-01 0.43043520
## StateMaine -0.123748761 1.993242e-02 0.16361360
## StateMaryland -1.738187896 -1.539511e+00 -1.34083426
## StateMassachusetts -0.343594890 -9.581610e-02 0.15196269
## StateMichigan -0.125622954 -3.275458e-02 0.06011379
## StateMinnesota -0.815653006 -7.107882e-01 -0.60592338
## StateMississippi -0.141559018 -4.987073e-02 0.04181756
## StateMissouri 0.073234663 1.644191e-01 0.25560348
## StateMontana -0.636430671 -5.025719e-01 -0.36871321
## StateNebraska -0.979013715 -8.788536e-01 -0.77869348
## StateNevada 0.263925040 4.032381e-01 0.54255124
## StateNew Hampshire 0.007532138 1.198117e-01 0.23209117
## StateNew Jersey -0.112177572 4.021439e-02 0.19260636
## StateNew Mexico 0.397124639 5.691988e-01 0.74127297
## StateNew York -0.277609783 -1.778175e-01 -0.07802516
## StateNorth Carolina 0.155235658 2.327622e-01 0.31028869
## StateNorth Dakota -1.304472017 -1.151218e+00 -0.99796355
## StateOhio 0.334026326 4.361814e-01 0.53833657
## StateOklahoma 0.339894506 4.533470e-01 0.56679950
## StateOregon -0.451327786 -3.275490e-01 -0.20377028
## StatePennsylvania 0.459766169 5.452425e-01 0.63071874
## StateRhode Island -0.673140069 -3.431727e-01 -0.01320542
## StateSouth Carolina 0.120718786 2.059469e-01 0.29117500
## StateSouth Dakota -1.154314365 -1.027659e+00 -0.90100282
## StateTennessee 0.387278412 4.674282e-01 0.54757791
## StateTexas -0.130893480 -2.100228e-02 0.08888893
## StateUtah -0.236806398 -1.021254e-01 0.03255555
## StateVermont -0.357143094 -2.267290e-01 -0.09631498
## StateVirginia -0.126891940 -3.502118e-02 0.05684958
## StateWashington -0.132368537 2.416598e-03 0.13720173
## StateWest Virginia 0.638723984 7.777861e-01 0.91684822
## StateWisconsin -0.077941341 5.882776e-03 0.08970689
## StateWyoming -0.139555529 -2.169648e-02 0.09616258
## factor(Time_Period_ID)2 -0.182683926 -4.193465e-03 0.17429700
## factor(Time_Period_ID)3 -0.054097599 1.132110e-01 0.28051968
## factor(Time_Period_ID)4 -0.007798426 1.622897e-01 0.33237780
## factor(Time_Period_ID)5 0.136392992 3.198863e-01 0.50337959
## factor(Time_Period_ID)6 0.158159228 3.396625e-01 0.52116568
## factor(Time_Period_ID)7 0.311954493 4.779435e-01 0.64393259
## factor(Time_Period_ID)8 0.289110842 4.620562e-01 0.63500165
## factor(Time_Period_ID)9 0.365445134 5.468409e-01 0.72823668
## factor(Time_Period_ID)10 0.365866689 5.439792e-01 0.72209165
## factor(Time_Period_ID)11 0.505418833 6.607149e-01 0.81601088
## factor(Time_Period_ID)12 0.512055077 6.756633e-01 0.83927155
## factor(Time_Period_ID)13 0.683555987 8.393450e-01 0.99513393
## factor(Time_Period_ID)14 0.730801858 8.890822e-01 1.04736259
## factor(Time_Period_ID)15 0.781954795 9.345076e-01 1.08706033
## factor(Time_Period_ID)16 0.792023636 9.465946e-01 1.10116548
## factor(Time_Period_ID)17 0.871937760 1.029370e+00 1.18680201
## factor(Time_Period_ID)18 0.876755453 1.030412e+00 1.18406954
## factor(Time_Period_ID)19 0.846352674 1.016078e+00 1.18580255
## factor(Time_Period_ID)20 0.862723196 1.020809e+00 1.17889498
## factor(Time_Period_ID)21 0.902948056 1.056862e+00 1.21077529
## factor(Time_Period_ID)22 0.864848395 1.023971e+00 1.18309393
## factor(Time_Period_ID)23 1.012982576 1.169317e+00 1.32565133
## factor(Time_Period_ID)24 1.002680392 1.162103e+00 1.32152554
## factor(Time_Period_ID)25 0.995257127 1.156757e+00 1.31825610
## factor(Time_Period_ID)26 0.998867395 1.159892e+00 1.32091599
## factor(Time_Period_ID)27 1.096272192 1.255040e+00 1.41380696
## factor(Time_Period_ID)28 1.064983223 1.224102e+00 1.38322132
## factor(Time_Period_ID)29 1.115437722 1.275260e+00 1.43508298
## factor(Time_Period_ID)30 1.122689703 1.282527e+00 1.44236405
## factor(Time_Period_ID)31 1.221448699 1.384571e+00 1.54769345
## factor(Time_Period_ID)32 1.247870688 1.414272e+00 1.58067383
## factor(Time_Period_ID)33 1.382490763 1.554408e+00 1.72632572
## factor(Time_Period_ID)34 1.405897173 1.582829e+00 1.75976183
## factor(Time_Period_ID)35 1.452521096 1.635433e+00 1.81834407
## factor(Time_Period_ID)36 1.462387545 1.643334e+00 1.82427984
## factor(Time_Period_ID)37 1.440588652 1.621393e+00 1.80219655
## factor(Time_Period_ID)38 1.412883856 1.593328e+00 1.77377281
## factor(Time_Period_ID)39 1.444375280 1.624170e+00 1.80396544
## factor(Time_Period_ID)40 1.505345068 1.683371e+00 1.86139770
## Naloxone_Pharmacy_Yes_Redefined -0.129703304 -5.661790e-02 0.01646751
## Naloxone_Pharmacy_No_Redefined -0.030506735 3.658799e-02 0.10368272
## Medical_Marijuana_Redefined 0.199087446 2.777546e-01 0.35642174
## Recreational_Marijuana_Redefined -0.346991479 -2.535416e-01 -0.16009181
## GSL_Redefined -0.011148894 4.494005e-02 0.10102899
## PDMP_Redefined -0.209301431 -1.514128e-01 -0.09352425
## Medicaid_Expansion_Redefined 0.039170120 9.274003e-02 0.14630994
## Intervention_Redefined -0.073425116 -2.813085e-02 0.01716341
## sd_coef
## (Intercept) 0.07575327
## StateAlaska 0.07172769
## StateArizona 0.06420650
## StateArkansas 0.05835211
## StateCalifornia 0.06897075
## StateColorado 0.06277320
## StateConnecticut 0.06285123
## StateDelaware 0.06070181
## StateFlorida 0.05323621
## StateGeorgia 0.04316293
## StateHawaii 0.06077735
## StateIdaho 0.04912707
## StateIllinois 0.05835190
## StateIndiana 0.05791328
## StateIowa 0.05064497
## StateKansas 0.04776005
## StateKentucky 0.04337366
## StateLouisiana 0.04616605
## StateMaine 0.07330672
## StateMaryland 0.10136572
## StateMassachusetts 0.12641775
## StateMichigan 0.04738182
## StateMinnesota 0.05350246
## StateMississippi 0.04677974
## StateMissouri 0.04652266
## StateMontana 0.06829527
## StateNebraska 0.05110210
## StateNevada 0.07107811
## StateNew Hampshire 0.05728547
## StateNew Jersey 0.07775100
## StateNew Mexico 0.08779294
## StateNew York 0.05091444
## StateNorth Carolina 0.03955435
## StateNorth Dakota 0.07819094
## StateOhio 0.05211996
## StateOklahoma 0.05788393
## StateOregon 0.06315242
## StatePennsylvania 0.04361035
## StateRhode Island 0.16835068
## StateSouth Carolina 0.04348373
## StateSouth Dakota 0.06462029
## StateTennessee 0.04089273
## StateTexas 0.05606694
## StateUtah 0.06871478
## StateVermont 0.06653778
## StateVirginia 0.04687284
## StateWashington 0.06876793
## StateWest Virginia 0.07095006
## StateWisconsin 0.04276741
## StateWyoming 0.06013217
## factor(Time_Period_ID)2 0.09106656
## factor(Time_Period_ID)3 0.08536155
## factor(Time_Period_ID)4 0.08677965
## factor(Time_Period_ID)5 0.09361903
## factor(Time_Period_ID)6 0.09260369
## factor(Time_Period_ID)7 0.08468829
## factor(Time_Period_ID)8 0.08823745
## factor(Time_Period_ID)9 0.09254886
## factor(Time_Period_ID)10 0.09087371
## factor(Time_Period_ID)11 0.07923267
## factor(Time_Period_ID)12 0.08347359
## factor(Time_Period_ID)13 0.07948417
## factor(Time_Period_ID)14 0.08075529
## factor(Time_Period_ID)15 0.07783304
## factor(Time_Period_ID)16 0.07886272
## factor(Time_Period_ID)17 0.08032251
## factor(Time_Period_ID)18 0.07839645
## factor(Time_Period_ID)19 0.08659436
## factor(Time_Period_ID)20 0.08065607
## factor(Time_Period_ID)21 0.07852736
## factor(Time_Period_ID)22 0.08118509
## factor(Time_Period_ID)23 0.07976244
## factor(Time_Period_ID)24 0.08133805
## factor(Time_Period_ID)25 0.08239770
## factor(Time_Period_ID)26 0.08215525
## factor(Time_Period_ID)27 0.08100377
## factor(Time_Period_ID)28 0.08118319
## factor(Time_Period_ID)29 0.08154216
## factor(Time_Period_ID)30 0.08154958
## factor(Time_Period_ID)31 0.08322570
## factor(Time_Period_ID)32 0.08489876
## factor(Time_Period_ID)33 0.08771300
## factor(Time_Period_ID)34 0.09027160
## factor(Time_Period_ID)35 0.09332219
## factor(Time_Period_ID)36 0.09231946
## factor(Time_Period_ID)37 0.09224691
## factor(Time_Period_ID)38 0.09206351
## factor(Time_Period_ID)39 0.09173218
## factor(Time_Period_ID)40 0.09082975
## Naloxone_Pharmacy_Yes_Redefined 0.03728847
## Naloxone_Pharmacy_No_Redefined 0.03423200
## Medical_Marijuana_Redefined 0.04013630
## Recreational_Marijuana_Redefined 0.04767849
## GSL_Redefined 0.02861681
## PDMP_Redefined 0.02953499
## Medicaid_Expansion_Redefined 0.02733159
## Intervention_Redefined 0.02310932
Event Study
Model Fitting
#create a formula for the gam model which includes the state effects, smoothed time effects, policy measures,
#the periods before the intervention (excluding 1 period and 34 periods before intervention)
#the intervention period, and the periods after the intervention
formula_event_study_log_fixed_time <- formula(paste("log(prop_dead) ~ State +
factor(Time_Period_ID) +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +",
paste(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)-2),
function(x)paste("neg_", x, "_pd", sep = "")), collapse = "+"),
"+",
paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_event_study_model_log_fixed_time<-lm(formula_event_study_log_fixed_time,
data = sensitivity_anlys_event_study_data)
summary(sensitivity_anlys_event_study_model_log_fixed_time)
##
## Call:
## lm(formula = formula_event_study_log_fixed_time, data = sensitivity_anlys_event_study_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.02228 -0.14569 0.01955 0.15652 0.95435
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.053e+01 9.794e-02 -107.541 < 2e-16 ***
## StateAlaska 2.324e-01 1.026e-01 2.266 0.023563 *
## StateArizona 3.166e-01 8.008e-02 3.954 7.99e-05 ***
## StateArkansas -4.549e-01 7.537e-02 -6.035 1.92e-09 ***
## StateCalifornia -2.766e-01 9.149e-02 -3.024 0.002530 **
## StateColorado 6.168e-02 8.383e-02 0.736 0.461975
## StateConnecticut 1.703e-01 7.466e-02 2.281 0.022668 *
## StateDelaware 2.950e-01 9.852e-02 2.995 0.002786 **
## StateFlorida 2.413e-01 9.039e-02 2.669 0.007667 **
## StateGeorgia -5.729e-02 9.630e-02 -0.595 0.551977
## StateHawaii -4.811e-01 9.031e-02 -5.327 1.12e-07 ***
## StateIdaho -5.384e-03 9.329e-02 -0.058 0.953986
## StateIllinois 7.740e-02 8.327e-02 0.930 0.352705
## StateIndiana 1.164e-01 7.200e-02 1.617 0.106035
## StateIowa -7.084e-01 7.636e-02 -9.276 < 2e-16 ***
## StateKansas -2.353e-01 7.001e-02 -3.361 0.000792 ***
## StateKentucky 7.580e-01 7.603e-02 9.970 < 2e-16 ***
## StateLouisiana 3.007e-01 7.715e-02 3.897 0.000101 ***
## StateMaine 4.097e-02 7.880e-02 0.520 0.603168
## StateMaryland -1.605e+00 8.451e-02 -18.996 < 2e-16 ***
## StateMassachusetts -9.130e-02 7.104e-02 -1.285 0.198864
## StateMichigan -4.462e-02 7.448e-02 -0.599 0.549138
## StateMinnesota -7.228e-01 7.345e-02 -9.841 < 2e-16 ***
## StateMississippi 5.152e-02 8.710e-02 0.591 0.554306
## StateMissouri 1.271e-01 7.561e-02 1.681 0.092868 .
## StateMontana -5.442e-01 8.034e-02 -6.774 1.69e-11 ***
## StateNebraska -8.068e-01 8.092e-02 -9.971 < 2e-16 ***
## StateNevada 3.921e-01 7.723e-02 5.077 4.22e-07 ***
## StateNew Hampshire 1.404e-01 7.249e-02 1.937 0.052925 .
## StateNew Jersey -2.221e-02 8.412e-02 -0.264 0.791765
## StateNew Mexico 5.982e-01 7.845e-02 7.626 3.87e-14 ***
## StateNew York -1.791e-01 7.218e-02 -2.482 0.013165 *
## StateNorth Carolina 2.069e-01 7.362e-02 2.811 0.004993 **
## StateNorth Dakota -1.080e+00 8.050e-02 -13.414 < 2e-16 ***
## StateOhio 3.845e-01 9.623e-02 3.996 6.69e-05 ***
## StateOklahoma 5.114e-01 7.480e-02 6.838 1.09e-11 ***
## StateOregon -3.107e-01 7.876e-02 -3.945 8.29e-05 ***
## StatePennsylvania 4.983e-01 8.998e-02 5.538 3.51e-08 ***
## StateRhode Island -2.431e-01 8.873e-02 -2.739 0.006215 **
## StateSouth Carolina 3.253e-01 9.485e-02 3.429 0.000618 ***
## StateSouth Dakota -9.065e-01 9.797e-02 -9.252 < 2e-16 ***
## StateTennessee 4.699e-01 6.941e-02 6.769 1.74e-11 ***
## StateTexas -6.328e-02 8.721e-02 -0.726 0.468195
## StateUtah -1.147e-01 7.245e-02 -1.584 0.113471
## StateVermont -2.100e-01 7.455e-02 -2.816 0.004908 **
## StateVirginia -7.392e-02 7.836e-02 -0.943 0.345611
## StateWashington 6.118e-03 7.875e-02 0.078 0.938083
## StateWest Virginia 8.577e-01 8.121e-02 10.562 < 2e-16 ***
## StateWisconsin -3.569e-02 7.727e-02 -0.462 0.644212
## StateWyoming 4.985e-03 7.093e-02 0.070 0.943980
## factor(Time_Period_ID)2 -8.285e-03 6.408e-02 -0.129 0.897144
## factor(Time_Period_ID)3 9.515e-02 6.476e-02 1.469 0.141941
## factor(Time_Period_ID)4 1.316e-01 6.412e-02 2.052 0.040324 *
## factor(Time_Period_ID)5 2.820e-01 6.545e-02 4.309 1.73e-05 ***
## factor(Time_Period_ID)6 2.904e-01 6.640e-02 4.374 1.29e-05 ***
## factor(Time_Period_ID)7 4.234e-01 6.702e-02 6.318 3.32e-10 ***
## factor(Time_Period_ID)8 3.970e-01 6.853e-02 5.792 8.16e-09 ***
## factor(Time_Period_ID)9 4.752e-01 6.989e-02 6.800 1.41e-11 ***
## factor(Time_Period_ID)10 4.632e-01 7.165e-02 6.465 1.30e-10 ***
## factor(Time_Period_ID)11 5.738e-01 7.352e-02 7.806 9.87e-15 ***
## factor(Time_Period_ID)12 5.842e-01 7.549e-02 7.740 1.64e-14 ***
## factor(Time_Period_ID)13 7.466e-01 7.760e-02 9.622 < 2e-16 ***
## factor(Time_Period_ID)14 7.828e-01 7.998e-02 9.788 < 2e-16 ***
## factor(Time_Period_ID)15 8.174e-01 8.218e-02 9.947 < 2e-16 ***
## factor(Time_Period_ID)16 8.321e-01 8.444e-02 9.854 < 2e-16 ***
## factor(Time_Period_ID)17 9.073e-01 8.736e-02 10.386 < 2e-16 ***
## factor(Time_Period_ID)18 9.009e-01 9.000e-02 10.010 < 2e-16 ***
## factor(Time_Period_ID)19 8.851e-01 9.260e-02 9.559 < 2e-16 ***
## factor(Time_Period_ID)20 8.812e-01 9.570e-02 9.208 < 2e-16 ***
## factor(Time_Period_ID)21 9.069e-01 9.865e-02 9.192 < 2e-16 ***
## factor(Time_Period_ID)22 8.747e-01 1.015e-01 8.616 < 2e-16 ***
## factor(Time_Period_ID)23 1.014e+00 1.047e-01 9.683 < 2e-16 ***
## factor(Time_Period_ID)24 1.007e+00 1.079e-01 9.335 < 2e-16 ***
## factor(Time_Period_ID)25 1.009e+00 1.110e-01 9.091 < 2e-16 ***
## factor(Time_Period_ID)26 1.004e+00 1.142e-01 8.791 < 2e-16 ***
## factor(Time_Period_ID)27 1.094e+00 1.174e-01 9.314 < 2e-16 ***
## factor(Time_Period_ID)28 1.059e+00 1.207e-01 8.777 < 2e-16 ***
## factor(Time_Period_ID)29 1.099e+00 1.255e-01 8.758 < 2e-16 ***
## factor(Time_Period_ID)30 1.107e+00 1.292e-01 8.566 < 2e-16 ***
## factor(Time_Period_ID)31 1.199e+00 1.328e-01 9.030 < 2e-16 ***
## factor(Time_Period_ID)32 1.221e+00 1.372e-01 8.904 < 2e-16 ***
## factor(Time_Period_ID)33 1.365e+00 1.413e-01 9.664 < 2e-16 ***
## factor(Time_Period_ID)34 1.381e+00 1.457e-01 9.481 < 2e-16 ***
## factor(Time_Period_ID)35 1.425e+00 1.490e-01 9.567 < 2e-16 ***
## factor(Time_Period_ID)36 1.440e+00 1.531e-01 9.403 < 2e-16 ***
## factor(Time_Period_ID)37 1.410e+00 1.565e-01 9.011 < 2e-16 ***
## factor(Time_Period_ID)38 1.383e+00 1.601e-01 8.636 < 2e-16 ***
## factor(Time_Period_ID)39 1.416e+00 1.639e-01 8.641 < 2e-16 ***
## factor(Time_Period_ID)40 1.474e+00 1.672e-01 8.818 < 2e-16 ***
## Naloxone_Pharmacy_Yes_Redefined -4.588e-02 4.649e-02 -0.987 0.323832
## Naloxone_Pharmacy_No_Redefined 3.276e-02 3.960e-02 0.827 0.408289
## Medical_Marijuana_Redefined 2.744e-01 3.157e-02 8.691 < 2e-16 ***
## Recreational_Marijuana_Redefined -2.668e-01 4.738e-02 -5.631 2.07e-08 ***
## GSL_Redefined 5.450e-02 3.295e-02 1.654 0.098347 .
## PDMP_Redefined -1.777e-01 2.646e-02 -6.717 2.47e-11 ***
## Medicaid_Expansion_Redefined 1.056e-01 3.257e-02 3.241 0.001212 **
## neg_2_pd 2.842e-02 6.450e-02 0.441 0.659514
## neg_3_pd 4.588e-03 6.563e-02 0.070 0.944274
## neg_4_pd -2.453e-02 6.646e-02 -0.369 0.712106
## neg_5_pd -3.613e-02 6.734e-02 -0.536 0.591692
## neg_6_pd -4.071e-02 6.962e-02 -0.585 0.558776
## neg_7_pd -9.720e-02 7.055e-02 -1.378 0.168450
## neg_8_pd -1.631e-01 7.233e-02 -2.255 0.024280 *
## neg_9_pd -1.185e-01 7.515e-02 -1.577 0.114987
## neg_10_pd -8.315e-02 7.745e-02 -1.074 0.283149
## neg_11_pd -8.336e-02 7.989e-02 -1.043 0.296875
## neg_12_pd -1.193e-02 8.433e-02 -0.141 0.887510
## neg_13_pd -1.133e-01 8.638e-02 -1.312 0.189697
## neg_14_pd -1.448e-01 8.865e-02 -1.634 0.102453
## neg_15_pd -1.933e-01 9.074e-02 -2.130 0.033316 *
## neg_16_pd -1.865e-01 9.492e-02 -1.965 0.049601 *
## neg_17_pd -1.805e-01 1.010e-01 -1.787 0.074138 .
## neg_18_pd -1.922e-01 1.043e-01 -1.843 0.065479 .
## neg_19_pd -3.035e-01 1.075e-01 -2.824 0.004801 **
## neg_20_pd -3.790e-01 1.141e-01 -3.321 0.000913 ***
## neg_21_pd -3.025e-01 1.215e-01 -2.489 0.012889 *
## neg_22_pd -2.874e-01 1.238e-01 -2.321 0.020378 *
## neg_23_pd -2.988e-01 1.284e-01 -2.327 0.020098 *
## neg_24_pd -3.796e-01 1.384e-01 -2.743 0.006139 **
## neg_25_pd -2.419e-01 1.407e-01 -1.719 0.085735 .
## neg_26_pd -2.266e-01 1.463e-01 -1.549 0.121546
## neg_27_pd -4.453e-01 1.631e-01 -2.730 0.006397 **
## neg_28_pd -4.520e-01 1.653e-01 -2.734 0.006314 **
## neg_29_pd -2.018e-01 1.750e-01 -1.153 0.249081
## neg_30_pd -2.525e-01 1.868e-01 -1.351 0.176702
## neg_31_pd -2.519e-01 1.890e-01 -1.333 0.182589
## neg_32_pd -2.585e-01 2.040e-01 -1.267 0.205234
## neg_33_pd -2.719e-01 2.593e-01 -1.049 0.294503
## pos_0_pd -9.966e-05 6.423e-02 -0.002 0.998762
## pos_1_pd -2.641e-02 6.490e-02 -0.407 0.684052
## pos_2_pd 2.020e-02 6.519e-02 0.310 0.756714
## pos_3_pd -5.337e-03 6.644e-02 -0.080 0.935983
## pos_4_pd 1.567e-03 6.758e-02 0.023 0.981502
## pos_5_pd -2.710e-02 6.895e-02 -0.393 0.694329
## pos_6_pd -2.756e-02 7.086e-02 -0.389 0.697357
## pos_7_pd -1.702e-02 7.268e-02 -0.234 0.814927
## pos_8_pd -3.948e-02 7.555e-02 -0.523 0.601354
## pos_9_pd -3.794e-02 7.803e-02 -0.486 0.626917
## pos_10_pd -4.375e-02 8.001e-02 -0.547 0.584554
## pos_11_pd -3.991e-02 8.275e-02 -0.482 0.629654
## pos_12_pd -3.796e-02 8.559e-02 -0.444 0.657448
## pos_13_pd -9.049e-02 8.808e-02 -1.027 0.304399
## pos_14_pd -6.580e-02 9.171e-02 -0.718 0.473133
## pos_15_pd -5.502e-02 9.511e-02 -0.578 0.563026
## pos_16_pd -5.159e-02 9.785e-02 -0.527 0.598071
## pos_17_pd -2.880e-02 1.018e-01 -0.283 0.777418
## pos_18_pd 1.626e-02 1.054e-01 0.154 0.877433
## pos_19_pd 2.997e-02 1.080e-01 0.277 0.781506
## pos_20_pd 4.163e-02 1.124e-01 0.370 0.711258
## pos_21_pd 2.602e-02 1.170e-01 0.222 0.824030
## pos_22_pd 2.513e-02 1.206e-01 0.208 0.834909
## pos_23_pd 1.943e-02 1.245e-01 0.156 0.875987
## pos_24_pd -3.386e-02 1.305e-01 -0.259 0.795310
## pos_25_pd 5.876e-03 1.361e-01 0.043 0.965569
## pos_26_pd 2.342e-02 1.393e-01 0.168 0.866536
## pos_27_pd -1.540e-02 1.428e-01 -0.108 0.914141
## pos_28_pd 1.567e-02 1.458e-01 0.107 0.914462
## pos_29_pd 3.032e-02 1.537e-01 0.197 0.843615
## pos_30_pd 8.008e-02 1.583e-01 0.506 0.613054
## pos_31_pd 1.375e-01 1.636e-01 0.841 0.400626
## pos_32_pd 1.034e-01 1.739e-01 0.594 0.552267
## pos_33_pd 9.727e-02 1.807e-01 0.538 0.590467
## pos_34_pd 1.147e-01 1.839e-01 0.624 0.532921
## pos_35_pd -6.920e-02 2.018e-01 -0.343 0.731649
## pos_36_pd -9.751e-02 2.047e-01 -0.476 0.633885
## pos_37_pd -5.381e-02 2.280e-01 -0.236 0.813430
## pos_38_pd -1.618e-02 2.809e-01 -0.058 0.954054
## pos_39_pd -7.100e-02 2.832e-01 -0.251 0.802039
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3099 on 1832 degrees of freedom
## Multiple R-squared: 0.8363, Adjusted R-squared: 0.8213
## F-statistic: 56.03 on 167 and 1832 DF, p-value: < 2.2e-16
Sandwich Estimator
#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_event_study_log_fixed_time <- model.matrix(sensitivity_anlys_event_study_model_log_fixed_time)
#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_event_study_log_fixed_time <- coef(sensitivity_anlys_event_study_model_log_fixed_time)
#type = "response" to get the estimated probabilities
sensitivity_anlys_event_study_sd_and_ci_log_fixed_time <-
compute_sd_and_CI((full_df_w_basis_functions_sensitivity_anlys_event_study_log_fixed_time),
log(sensitivity_anlys_event_study_data$prop_dead),
coefficient_values_sensitivity_anlys_event_study_log_fixed_time,
p = ncol(full_df_w_basis_functions_sensitivity_anlys_event_study_log_fixed_time) - 50)
(sensitivity_anlys_event_study_sd_and_ci_log_fixed_time)
## lb_coef coef_values ub_coef
## (Intercept) -10.729822917 -1.053284e+01 -10.335859558
## StateAlaska 0.054172688 2.323927e-01 0.410612739
## StateArizona 0.170267751 3.166173e-01 0.462966918
## StateArkansas -0.568347675 -4.548515e-01 -0.341355289
## StateCalifornia -0.432485956 -2.766479e-01 -0.120809850
## StateColorado -0.074937939 6.167797e-02 0.198293878
## StateConnecticut 0.044472662 1.702845e-01 0.296096305
## StateDelaware 0.141709808 2.950337e-01 0.448357616
## StateFlorida 0.107469795 2.412924e-01 0.375114923
## StateGeorgia -0.190014286 -5.729004e-02 0.075434201
## StateHawaii -0.620522703 -4.811223e-01 -0.341721945
## StateIdaho -0.151413956 -5.383928e-03 0.140646099
## StateIllinois -0.052536841 7.740347e-02 0.207343782
## StateIndiana 0.004043564 1.164288e-01 0.228813986
## StateIowa -0.830486766 -7.083535e-01 -0.586220323
## StateKansas -0.332741287 -2.353032e-01 -0.137865208
## StateKentucky 0.660051210 7.580209e-01 0.855990600
## StateLouisiana 0.193327284 3.006912e-01 0.408055106
## StateMaine -0.110790892 4.096916e-02 0.192729208
## StateMaryland -1.820581271 -1.605356e+00 -1.390130259
## StateMassachusetts -0.340760428 -9.130156e-02 0.158157304
## StateMichigan -0.143557790 -4.462401e-02 0.054309774
## StateMinnesota -0.834357418 -7.228330e-01 -0.611308554
## StateMississippi -0.083209611 5.151543e-02 0.186240462
## StateMissouri 0.022281284 1.271294e-01 0.231977592
## StateMontana -0.683838462 -5.441789e-01 -0.404519244
## StateNebraska -0.922594757 -8.068464e-01 -0.691098116
## StateNevada 0.249787292 3.921379e-01 0.534488518
## StateNew Hampshire 0.021838627 1.403922e-01 0.258945830
## StateNew Jersey -0.185139897 -2.221187e-02 0.140716152
## StateNew Mexico 0.415847614 5.982206e-01 0.780593579
## StateNew York -0.281543924 -1.791234e-01 -0.076702829
## StateNorth Carolina 0.117383420 2.069288e-01 0.296474120
## StateNorth Dakota -1.248935424 -1.079797e+00 -0.910658399
## StateOhio 0.230727211 3.845419e-01 0.538356685
## StateOklahoma 0.389192360 5.114345e-01 0.633676641
## StateOregon -0.438805257 -3.106916e-01 -0.182577884
## StatePennsylvania 0.377698079 4.982749e-01 0.618851700
## StateRhode Island -0.551525979 -2.430720e-01 0.065382040
## StateSouth Carolina 0.189968848 3.252890e-01 0.460609145
## StateSouth Dakota -1.074149221 -9.064547e-01 -0.738760186
## StateTennessee 0.383632643 4.698579e-01 0.556083105
## StateTexas -0.195105528 -6.327772e-02 0.068550094
## StateUtah -0.264457420 -1.147339e-01 0.034989521
## StateVermont -0.344753613 -2.099737e-01 -0.075193713
## StateVirginia -0.178738571 -7.392103e-02 0.030896511
## StateWashington -0.131596796 6.117690e-03 0.143832176
## StateWest Virginia 0.709111451 8.576940e-01 1.006276620
## StateWisconsin -0.141909582 -3.569278e-02 0.070524014
## StateWyoming -0.114418061 4.984789e-03 0.124387638
## factor(Time_Period_ID)2 -0.185613676 -8.284615e-03 0.169044446
## factor(Time_Period_ID)3 -0.077695631 9.515333e-02 0.268002288
## factor(Time_Period_ID)4 -0.039995457 1.315751e-01 0.303145756
## factor(Time_Period_ID)5 0.093433280 2.820032e-01 0.470573215
## factor(Time_Period_ID)6 0.093280044 2.904193e-01 0.487558603
## factor(Time_Period_ID)7 0.252091912 4.234193e-01 0.594746691
## factor(Time_Period_ID)8 0.222405605 3.969617e-01 0.571517781
## factor(Time_Period_ID)9 0.286735480 4.752227e-01 0.663710011
## factor(Time_Period_ID)10 0.274963928 4.631810e-01 0.651398129
## factor(Time_Period_ID)11 0.409700937 5.738495e-01 0.737998069
## factor(Time_Period_ID)12 0.413066294 5.842444e-01 0.755422509
## factor(Time_Period_ID)13 0.579991122 7.466213e-01 0.913251427
## factor(Time_Period_ID)14 0.610574663 7.828297e-01 0.955084712
## factor(Time_Period_ID)15 0.650812359 8.174001e-01 0.983987888
## factor(Time_Period_ID)16 0.661875743 8.321066e-01 1.002337412
## factor(Time_Period_ID)17 0.731882165 9.073307e-01 1.082779285
## factor(Time_Period_ID)18 0.726252701 9.008909e-01 1.075529002
## factor(Time_Period_ID)19 0.694999680 8.851166e-01 1.075233610
## factor(Time_Period_ID)20 0.696926890 8.811826e-01 1.065438407
## factor(Time_Period_ID)21 0.723505825 9.068531e-01 1.090200277
## factor(Time_Period_ID)22 0.683822472 8.747203e-01 1.065618097
## factor(Time_Period_ID)23 0.822566173 1.013657e+00 1.204748514
## factor(Time_Period_ID)24 0.810315411 1.007054e+00 1.203793339
## factor(Time_Period_ID)25 0.807181835 1.008954e+00 1.210725522
## factor(Time_Period_ID)26 0.797761118 1.003976e+00 1.210191767
## factor(Time_Period_ID)27 0.887253689 1.093706e+00 1.300158380
## factor(Time_Period_ID)28 0.847506641 1.059129e+00 1.270750477
## factor(Time_Period_ID)29 0.881240671 1.099261e+00 1.317280687
## factor(Time_Period_ID)30 0.883986738 1.106560e+00 1.329134253
## factor(Time_Period_ID)31 0.970227722 1.198997e+00 1.427765817
## factor(Time_Period_ID)32 0.987364421 1.221435e+00 1.455505258
## factor(Time_Period_ID)33 1.124281297 1.365204e+00 1.606125890
## factor(Time_Period_ID)34 1.133100986 1.381331e+00 1.629561886
## factor(Time_Period_ID)35 1.166984332 1.425255e+00 1.683525341
## factor(Time_Period_ID)36 1.179270897 1.439727e+00 1.700182625
## factor(Time_Period_ID)37 1.145827343 1.410226e+00 1.674623837
## factor(Time_Period_ID)38 1.113581095 1.382541e+00 1.651501622
## factor(Time_Period_ID)39 1.143068642 1.415995e+00 1.688922118
## factor(Time_Period_ID)40 1.198384668 1.474234e+00 1.750083268
## Naloxone_Pharmacy_Yes_Redefined -0.119376311 -4.588103e-02 0.027614254
## Naloxone_Pharmacy_No_Redefined -0.036005115 3.275524e-02 0.101515586
## Medical_Marijuana_Redefined 0.194971756 2.744189e-01 0.353866106
## Recreational_Marijuana_Redefined -0.362989288 -2.668305e-01 -0.170671766
## GSL_Redefined -0.003413345 5.449834e-02 0.112410016
## PDMP_Redefined -0.238570986 -1.777134e-01 -0.116855721
## Medicaid_Expansion_Redefined 0.049972645 1.055728e-01 0.161172955
## neg_2_pd -0.082381838 2.842348e-02 0.139228801
## neg_3_pd -0.110294880 4.588085e-03 0.119471050
## neg_4_pd -0.143934103 -2.452977e-02 0.094874563
## neg_5_pd -0.152141932 -3.612539e-02 0.079891152
## neg_6_pd -0.157291283 -4.071050e-02 0.075870277
## neg_7_pd -0.216961288 -9.720499e-02 0.022551303
## neg_8_pd -0.311300104 -1.630612e-01 -0.014822393
## neg_9_pd -0.277368199 -1.185041e-01 0.040359925
## neg_10_pd -0.231863683 -8.314656e-02 0.065570568
## neg_11_pd -0.241548942 -8.335927e-02 0.074830405
## neg_12_pd -0.187872406 -1.193000e-02 0.164012406
## neg_13_pd -0.292118767 -1.133316e-01 0.065455479
## neg_14_pd -0.322018833 -1.448378e-01 0.032343181
## neg_15_pd -0.401176261 -1.932577e-01 0.014660903
## neg_16_pd -0.387587796 -1.864842e-01 0.014619443
## neg_17_pd -0.365468925 -1.805327e-01 0.004403501
## neg_18_pd -0.371454398 -1.921785e-01 -0.012902518
## neg_19_pd -0.573235279 -3.035347e-01 -0.033834048
## neg_20_pd -0.692949454 -3.789875e-01 -0.065025477
## neg_21_pd -0.537832807 -3.024593e-01 -0.067085797
## neg_22_pd -0.540851052 -2.873767e-01 -0.033902419
## neg_23_pd -0.640613094 -2.987530e-01 0.043107028
## neg_24_pd -0.789721271 -3.795698e-01 0.030581669
## neg_25_pd -0.578611412 -2.419419e-01 0.094727623
## neg_26_pd -0.618467889 -2.266129e-01 0.165242179
## neg_27_pd -1.010215002 -4.452797e-01 0.119655644
## neg_28_pd -1.025870029 -4.520347e-01 0.121800545
## neg_29_pd -0.581810980 -2.018027e-01 0.178205608
## neg_30_pd -0.603349715 -2.525073e-01 0.098335102
## neg_31_pd -0.533605111 -2.519349e-01 0.029735393
## neg_32_pd -0.568068910 -2.584989e-01 0.051071072
## neg_33_pd -0.640899674 -2.718532e-01 0.097193207
## pos_0_pd -0.106009954 -9.965934e-05 0.105810635
## pos_1_pd -0.141197407 -2.641429e-02 0.088368817
## pos_2_pd -0.084217175 2.019822e-02 0.124613608
## pos_3_pd -0.111115132 -5.336848e-03 0.100441435
## pos_4_pd -0.106262518 1.567118e-03 0.109396755
## pos_5_pd -0.135836515 -2.710068e-02 0.081635154
## pos_6_pd -0.140323601 -2.755982e-02 0.085203971
## pos_7_pd -0.135286509 -1.701538e-02 0.101255742
## pos_8_pd -0.152867258 -3.947891e-02 0.073909438
## pos_9_pd -0.160141919 -3.793528e-02 0.084271362
## pos_10_pd -0.171398614 -4.375081e-02 0.083896986
## pos_11_pd -0.159818092 -3.991163e-02 0.079994835
## pos_12_pd -0.162396258 -3.795940e-02 0.086477456
## pos_13_pd -0.232035112 -9.049109e-02 0.051052937
## pos_14_pd -0.210024781 -6.580435e-02 0.078416078
## pos_15_pd -0.202962942 -5.501595e-02 0.092931033
## pos_16_pd -0.202208346 -5.159255e-02 0.099023236
## pos_17_pd -0.190587955 -2.879518e-02 0.132997597
## pos_18_pd -0.148561848 1.625955e-02 0.181080958
## pos_19_pd -0.128156389 2.996664e-02 0.188089663
## pos_20_pd -0.125065171 4.162673e-02 0.208318630
## pos_21_pd -0.149339949 2.602476e-02 0.201389466
## pos_22_pd -0.150137811 2.513029e-02 0.200398384
## pos_23_pd -0.160747281 1.942726e-02 0.199601797
## pos_24_pd -0.219782680 -3.385570e-02 0.152071285
## pos_25_pd -0.197009528 5.876321e-03 0.208762170
## pos_26_pd -0.179446782 2.341892e-02 0.226284623
## pos_27_pd -0.238902512 -1.540153e-02 0.208099451
## pos_28_pd -0.211932620 1.566547e-02 0.243263562
## pos_29_pd -0.217174774 3.031926e-02 0.277813301
## pos_30_pd -0.176984121 8.008246e-02 0.337149044
## pos_31_pd -0.143971113 1.375114e-01 0.418994004
## pos_32_pd -0.178568702 1.033884e-01 0.385345418
## pos_33_pd -0.220811762 9.727439e-02 0.415360537
## pos_34_pd -0.200288717 1.146659e-01 0.429620443
## pos_35_pd -0.337731577 -6.920026e-02 0.199331055
## pos_36_pd -0.360359328 -9.750608e-02 0.165347160
## pos_37_pd -0.321532694 -5.381403e-02 0.213904627
## pos_38_pd -0.300410958 -1.618438e-02 0.268042190
## pos_39_pd -0.421317872 -7.100497e-02 0.279307923
## sd_coef
## (Intercept) 0.10050086
## StateAlaska 0.09092858
## StateArizona 0.07466815
## StateArkansas 0.05790622
## StateCalifornia 0.07950921
## StateColorado 0.06970199
## StateConnecticut 0.06418971
## StateDelaware 0.07822648
## StateFlorida 0.06827682
## StateGeorgia 0.06771645
## StateHawaii 0.07112264
## StateIdaho 0.07450512
## StateIllinois 0.06629608
## StateIndiana 0.05733939
## StateIowa 0.06231287
## StateKansas 0.04971329
## StateKentucky 0.04998454
## StateLouisiana 0.05477751
## StateMaine 0.07742860
## StateMaryland 0.10980893
## StateMassachusetts 0.12727493
## StateMichigan 0.05047642
## StateMinnesota 0.05690022
## StateMississippi 0.06873726
## StateMissouri 0.05349396
## StateMontana 0.07125490
## StateNebraska 0.05905527
## StateNevada 0.07262786
## StateNew Hampshire 0.06048653
## StateNew Jersey 0.08312654
## StateNew Mexico 0.09304744
## StateNew York 0.05225538
## StateNorth Carolina 0.04568640
## StateNorth Dakota 0.08629516
## StateOhio 0.07847691
## StateOklahoma 0.06236844
## StateOregon 0.06536413
## StatePennsylvania 0.06151878
## StateRhode Island 0.15737449
## StateSouth Carolina 0.06904089
## StateSouth Dakota 0.08555843
## StateTennessee 0.04399246
## StateTexas 0.06725909
## StateUtah 0.07638953
## StateVermont 0.06876528
## StateVirginia 0.05347834
## StateWashington 0.07026249
## StateWest Virginia 0.07580744
## StateWisconsin 0.05419224
## StateWyoming 0.06091982
## factor(Time_Period_ID)2 0.09047401
## factor(Time_Period_ID)3 0.08818824
## factor(Time_Period_ID)4 0.08753602
## factor(Time_Period_ID)5 0.09620917
## factor(Time_Period_ID)6 0.10058126
## factor(Time_Period_ID)7 0.08741193
## factor(Time_Period_ID)8 0.08905923
## factor(Time_Period_ID)9 0.09616697
## factor(Time_Period_ID)10 0.09602913
## factor(Time_Period_ID)11 0.08374927
## factor(Time_Period_ID)12 0.08733577
## factor(Time_Period_ID)13 0.08501538
## factor(Time_Period_ID)14 0.08788522
## factor(Time_Period_ID)15 0.08499376
## factor(Time_Period_ID)16 0.08685247
## factor(Time_Period_ID)17 0.08951457
## factor(Time_Period_ID)18 0.08910110
## factor(Time_Period_ID)19 0.09699845
## factor(Time_Period_ID)20 0.09400804
## factor(Time_Period_ID)21 0.09354450
## factor(Time_Period_ID)22 0.09739684
## factor(Time_Period_ID)23 0.09749550
## factor(Time_Period_ID)24 0.10037702
## factor(Time_Period_ID)25 0.10294482
## factor(Time_Period_ID)26 0.10521190
## factor(Time_Period_ID)27 0.10533283
## factor(Time_Period_ID)28 0.10797037
## factor(Time_Period_ID)29 0.11123470
## factor(Time_Period_ID)30 0.11355804
## factor(Time_Period_ID)31 0.11671890
## factor(Time_Period_ID)32 0.11942368
## factor(Time_Period_ID)33 0.12291954
## factor(Time_Period_ID)34 0.12664819
## factor(Time_Period_ID)35 0.13177067
## factor(Time_Period_ID)36 0.13288564
## factor(Time_Period_ID)37 0.13489706
## factor(Time_Period_ID)38 0.13722462
## factor(Time_Period_ID)39 0.13924834
## factor(Time_Period_ID)40 0.14073944
## Naloxone_Pharmacy_Yes_Redefined 0.03749759
## Naloxone_Pharmacy_No_Redefined 0.03508181
## Medical_Marijuana_Redefined 0.04053427
## Recreational_Marijuana_Redefined 0.04906059
## GSL_Redefined 0.02954678
## PDMP_Redefined 0.03104981
## Medicaid_Expansion_Redefined 0.02836743
## neg_2_pd 0.05653333
## neg_3_pd 0.05861376
## neg_4_pd 0.06092058
## neg_5_pd 0.05919211
## neg_6_pd 0.05947999
## neg_7_pd 0.06110015
## neg_8_pd 0.07563207
## neg_9_pd 0.08105309
## neg_10_pd 0.07587608
## neg_11_pd 0.08070902
## neg_12_pd 0.08976653
## neg_13_pd 0.09121792
## neg_14_pd 0.09039847
## neg_15_pd 0.10608091
## neg_16_pd 0.10260389
## neg_17_pd 0.09435521
## neg_18_pd 0.09146732
## neg_19_pd 0.13760235
## neg_20_pd 0.16018469
## neg_21_pd 0.12008852
## neg_22_pd 0.12932363
## neg_23_pd 0.17441840
## neg_24_pd 0.20926095
## neg_25_pd 0.17177016
## neg_26_pd 0.19992604
## neg_27_pd 0.28823231
## neg_28_pd 0.29277311
## neg_29_pd 0.19388178
## neg_30_pd 0.17900123
## neg_31_pd 0.14370931
## neg_32_pd 0.15794387
## neg_33_pd 0.18828900
## pos_0_pd 0.05403586
## pos_1_pd 0.05856281
## pos_2_pd 0.05327316
## pos_3_pd 0.05396851
## pos_4_pd 0.05501512
## pos_5_pd 0.05547747
## pos_6_pd 0.05753254
## pos_7_pd 0.06034241
## pos_8_pd 0.05785120
## pos_9_pd 0.06235033
## pos_10_pd 0.06512643
## pos_11_pd 0.06117677
## pos_12_pd 0.06348819
## pos_13_pd 0.07221634
## pos_14_pd 0.07358185
## pos_15_pd 0.07548316
## pos_16_pd 0.07684479
## pos_17_pd 0.08254733
## pos_18_pd 0.08409255
## pos_19_pd 0.08067501
## pos_20_pd 0.08504689
## pos_21_pd 0.08947179
## pos_22_pd 0.08942250
## pos_23_pd 0.09192579
## pos_24_pd 0.09486071
## pos_25_pd 0.10351319
## pos_26_pd 0.10350291
## pos_27_pd 0.11403111
## pos_28_pd 0.11612148
## pos_29_pd 0.12627247
## pos_30_pd 0.13115642
## pos_31_pd 0.14361355
## pos_32_pd 0.14385564
## pos_33_pd 0.16228885
## pos_34_pd 0.16069111
## pos_35_pd 0.13700577
## pos_36_pd 0.13410880
## pos_37_pd 0.13659115
## pos_38_pd 0.14501356
## pos_39_pd 0.17873107
# write.csv(round(sensitivity_anlys_event_study_sd_and_ci, 3), "./Data/event_study_coef_and_ci.csv")
Plot Results
#plot the coefficients for the periods before and after the intervention with 95% CI
plot_event_study_log_fixed_time <- sensitivity_anlys_event_study_sd_and_ci_log_fixed_time %>%
mutate(term = rownames(sensitivity_anlys_event_study_sd_and_ci_log_fixed_time)) %>%
dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
filter(term %in% c(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2),
function(x){paste("neg_", x, "_pd", sep = "")}),
sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_event_study_log_fixed_time) <- c("term", "estimate", "conf.low", "conf.high")
dwplot(plot_event_study_log_fixed_time, colour = "black",
vars_order = c(sapply((max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0,
function(x){paste("pos_", x, "_pd", sep = "")}),
sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2),
function(x){paste("neg_", x, "_pd", sep = "")}))) +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black"),
axis.text.x = element_text(angle = 45)) +
geom_vline(aes(xintercept = 0), linetype = "dashed") +
labs(y = "States Excluded", x = "Coefficients and 95% Confidence Intervals",
title = "Coefficient of Pre-Intervention and Post-Intervention Periods") +
scale_color_grey() +
coord_flip() +
geom_hline(yintercept = 33, col = "red", linetype = "dashed")
Analysis With Only Periods After Treatment
formula_post_tx_log_fixed_time <- formula(paste("log(prop_dead)~ State +
factor(Time_Period_ID) +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +",
paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_post_tx_model_log_fixed_time<-lm(formula_post_tx_log_fixed_time,
data = sensitivity_anlys_event_study_data)
summary(sensitivity_anlys_post_tx_model_log_fixed_time)
##
## Call:
## lm(formula = formula_post_tx_log_fixed_time, data = sensitivity_anlys_event_study_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.10074 -0.14327 0.01533 0.15938 0.94853
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -10.702051 0.066574 -160.754 < 2e-16 ***
## StateAlaska 0.031180 0.079305 0.393 0.694238
## StateArizona 0.200914 0.072119 2.786 0.005392 **
## StateArkansas -0.539628 0.071000 -7.600 4.65e-14 ***
## StateCalifornia -0.142773 0.080171 -1.781 0.075100 .
## StateColorado -0.041236 0.077986 -0.529 0.597036
## StateConnecticut 0.171073 0.074642 2.292 0.022021 *
## StateDelaware 0.096475 0.073288 1.316 0.188207
## StateFlorida 0.400005 0.074168 5.393 7.80e-08 ***
## StateGeorgia 0.125678 0.075840 1.657 0.097657 .
## StateHawaii -0.546050 0.078391 -6.966 4.51e-12 ***
## StateIdaho -0.191458 0.071702 -2.670 0.007647 **
## StateIllinois 0.197690 0.073388 2.694 0.007128 **
## StateIndiana 0.064618 0.070335 0.919 0.358360
## StateIowa -0.627597 0.071207 -8.814 < 2e-16 ***
## StateKansas -0.221516 0.069868 -3.170 0.001547 **
## StateKentucky 0.667804 0.071064 9.397 < 2e-16 ***
## StateLouisiana 0.391731 0.070770 5.535 3.55e-08 ***
## StateMaine 0.002399 0.077764 0.031 0.975393
## StateMaryland -1.476507 0.073289 -20.146 < 2e-16 ***
## StateMassachusetts -0.097092 0.071028 -1.367 0.171806
## StateMichigan 0.002758 0.072547 0.038 0.969681
## StateMinnesota -0.713219 0.073347 -9.724 < 2e-16 ***
## StateMississippi -0.112658 0.070845 -1.590 0.111959
## StateMissouri 0.190079 0.072468 2.623 0.008788 **
## StateMontana -0.459116 0.074860 -6.133 1.05e-09 ***
## StateNebraska -0.928373 0.071698 -12.948 < 2e-16 ***
## StateNevada 0.433983 0.075705 5.733 1.15e-08 ***
## StateNew Hampshire 0.092263 0.071080 1.298 0.194442
## StateNew Jersey 0.103757 0.073357 1.414 0.157408
## StateNew Mexico 0.539876 0.076524 7.055 2.42e-12 ***
## StateNew York -0.171359 0.072121 -2.376 0.017602 *
## StateNorth Carolina 0.271801 0.070129 3.876 0.000110 ***
## StateNorth Dakota -1.202645 0.071009 -16.936 < 2e-16 ***
## StateOhio 0.565722 0.076102 7.434 1.60e-13 ***
## StateOklahoma 0.428515 0.070576 6.072 1.53e-09 ***
## StateOregon -0.356845 0.077387 -4.611 4.28e-06 ***
## StatePennsylvania 0.653720 0.074362 8.791 < 2e-16 ***
## StateRhode Island -0.407196 0.074006 -5.502 4.27e-08 ***
## StateSouth Carolina 0.134528 0.071476 1.882 0.059972 .
## StateSouth Dakota -1.105675 0.072118 -15.332 < 2e-16 ***
## StateTennessee 0.468106 0.069431 6.742 2.08e-11 ***
## StateTexas 0.079895 0.073768 1.083 0.278920
## StateUtah -0.064121 0.070266 -0.913 0.361595
## StateVermont -0.253026 0.073321 -3.451 0.000571 ***
## StateVirginia 0.025975 0.071111 0.365 0.714947
## StateWashington -0.015154 0.078407 -0.193 0.846764
## StateWest Virginia 0.731595 0.071295 10.261 < 2e-16 ***
## StateWisconsin 0.055446 0.070901 0.782 0.434305
## StateWyoming -0.032838 0.069908 -0.470 0.638605
## factor(Time_Period_ID)2 -0.003472 0.062055 -0.056 0.955387
## factor(Time_Period_ID)3 0.111961 0.062045 1.805 0.071311 .
## factor(Time_Period_ID)4 0.163363 0.062099 2.631 0.008592 **
## factor(Time_Period_ID)5 0.320779 0.062165 5.160 2.73e-07 ***
## factor(Time_Period_ID)6 0.341605 0.062198 5.492 4.51e-08 ***
## factor(Time_Period_ID)7 0.484414 0.062301 7.775 1.23e-14 ***
## factor(Time_Period_ID)8 0.468420 0.062342 7.514 8.87e-14 ***
## factor(Time_Period_ID)9 0.559103 0.062466 8.951 < 2e-16 ***
## factor(Time_Period_ID)10 0.557941 0.062667 8.903 < 2e-16 ***
## factor(Time_Period_ID)11 0.678364 0.062819 10.799 < 2e-16 ***
## factor(Time_Period_ID)12 0.698451 0.063195 11.052 < 2e-16 ***
## factor(Time_Period_ID)13 0.867208 0.063499 13.657 < 2e-16 ***
## factor(Time_Period_ID)14 0.924458 0.063858 14.477 < 2e-16 ***
## factor(Time_Period_ID)15 0.975280 0.063958 15.249 < 2e-16 ***
## factor(Time_Period_ID)16 0.993784 0.064441 15.421 < 2e-16 ***
## factor(Time_Period_ID)17 1.086073 0.065089 16.686 < 2e-16 ***
## factor(Time_Period_ID)18 1.089873 0.065578 16.619 < 2e-16 ***
## factor(Time_Period_ID)19 1.079777 0.065950 16.373 < 2e-16 ***
## factor(Time_Period_ID)20 1.090787 0.066638 16.369 < 2e-16 ***
## factor(Time_Period_ID)21 1.132574 0.067332 16.821 < 2e-16 ***
## factor(Time_Period_ID)22 1.109169 0.067993 16.313 < 2e-16 ***
## factor(Time_Period_ID)23 1.257962 0.068652 18.324 < 2e-16 ***
## factor(Time_Period_ID)24 1.258759 0.069883 18.012 < 2e-16 ***
## factor(Time_Period_ID)25 1.269185 0.070409 18.026 < 2e-16 ***
## factor(Time_Period_ID)26 1.274017 0.071281 17.873 < 2e-16 ***
## factor(Time_Period_ID)27 1.376345 0.072403 19.009 < 2e-16 ***
## factor(Time_Period_ID)28 1.353182 0.073443 18.425 < 2e-16 ***
## factor(Time_Period_ID)29 1.409813 0.074810 18.845 < 2e-16 ***
## factor(Time_Period_ID)30 1.428426 0.076494 18.674 < 2e-16 ***
## factor(Time_Period_ID)31 1.532155 0.077671 19.726 < 2e-16 ***
## factor(Time_Period_ID)32 1.563880 0.080984 19.311 < 2e-16 ***
## factor(Time_Period_ID)33 1.718276 0.083272 20.634 < 2e-16 ***
## factor(Time_Period_ID)34 1.743618 0.086530 20.150 < 2e-16 ***
## factor(Time_Period_ID)35 1.797158 0.088028 20.416 < 2e-16 ***
## factor(Time_Period_ID)36 1.822423 0.090296 20.183 < 2e-16 ***
## factor(Time_Period_ID)37 1.804127 0.091132 19.797 < 2e-16 ***
## factor(Time_Period_ID)38 1.787316 0.092542 19.314 < 2e-16 ***
## factor(Time_Period_ID)39 1.831885 0.094029 19.482 < 2e-16 ***
## factor(Time_Period_ID)40 1.900976 0.094802 20.052 < 2e-16 ***
## Naloxone_Pharmacy_Yes_Redefined -0.039833 0.046410 -0.858 0.390836
## Naloxone_Pharmacy_No_Redefined 0.036536 0.039472 0.926 0.354756
## Medical_Marijuana_Redefined 0.287444 0.031264 9.194 < 2e-16 ***
## Recreational_Marijuana_Redefined -0.254885 0.047177 -5.403 7.41e-08 ***
## GSL_Redefined 0.052181 0.032901 1.586 0.112910
## PDMP_Redefined -0.165376 0.026052 -6.348 2.73e-10 ***
## Medicaid_Expansion_Redefined 0.091531 0.032270 2.836 0.004612 **
## pos_0_pd -0.011231 0.048953 -0.229 0.818565
## pos_1_pd -0.048451 0.049395 -0.981 0.326778
## pos_2_pd -0.012932 0.049820 -0.260 0.795219
## pos_3_pd -0.050056 0.050424 -0.993 0.320991
## pos_4_pd -0.053861 0.051030 -1.055 0.291339
## pos_5_pd -0.093673 0.051811 -1.808 0.070773 .
## pos_6_pd -0.104939 0.052810 -1.987 0.047054 *
## pos_7_pd -0.104506 0.053756 -1.944 0.052036 .
## pos_8_pd -0.139565 0.055417 -2.518 0.011870 *
## pos_9_pd -0.149774 0.056616 -2.645 0.008227 **
## pos_10_pd -0.166228 0.057380 -2.897 0.003812 **
## pos_11_pd -0.175784 0.058660 -2.997 0.002765 **
## pos_12_pd -0.185499 0.059876 -3.098 0.001977 **
## pos_13_pd -0.248970 0.060684 -4.103 4.26e-05 ***
## pos_14_pd -0.236852 0.063027 -3.758 0.000177 ***
## pos_15_pd -0.237447 0.064595 -3.676 0.000244 ***
## pos_16_pd -0.245207 0.065560 -3.740 0.000189 ***
## pos_17_pd -0.235199 0.068093 -3.454 0.000565 ***
## pos_18_pd -0.201209 0.069771 -2.884 0.003973 **
## pos_19_pd -0.197819 0.070714 -2.797 0.005204 **
## pos_20_pd -0.198499 0.073765 -2.691 0.007188 **
## pos_21_pd -0.224746 0.076944 -2.921 0.003532 **
## pos_22_pd -0.237068 0.078852 -3.006 0.002678 **
## pos_23_pd -0.254062 0.080859 -3.142 0.001704 **
## pos_24_pd -0.317806 0.086316 -3.682 0.000238 ***
## pos_25_pd -0.288596 0.091386 -3.158 0.001614 **
## pos_26_pd -0.282744 0.092343 -3.062 0.002231 **
## pos_27_pd -0.334363 0.093438 -3.578 0.000354 ***
## pos_28_pd -0.313426 0.094647 -3.312 0.000946 ***
## pos_29_pd -0.308766 0.103231 -2.991 0.002817 **
## pos_30_pd -0.270214 0.106554 -2.536 0.011296 *
## pos_31_pd -0.225267 0.110272 -2.043 0.041209 *
## pos_32_pd -0.271775 0.121608 -2.235 0.025546 *
## pos_33_pd -0.291040 0.127365 -2.285 0.022419 *
## pos_34_pd -0.284751 0.128405 -2.218 0.026702 *
## pos_35_pd -0.480443 0.149709 -3.209 0.001354 **
## pos_36_pd -0.519807 0.150596 -3.452 0.000570 ***
## pos_37_pd -0.488755 0.178091 -2.744 0.006120 **
## pos_38_pd -0.460498 0.240227 -1.917 0.055400 .
## pos_39_pd -0.526171 0.240905 -2.184 0.029076 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.31 on 1864 degrees of freedom
## Multiple R-squared: 0.8333, Adjusted R-squared: 0.8212
## F-statistic: 69.02 on 135 and 1864 DF, p-value: < 2.2e-16
Sandwich Estimator
#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_time <- model.matrix(sensitivity_anlys_post_tx_model_log_fixed_time)
#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_post_tx_log_fixed_time <- coef(sensitivity_anlys_post_tx_model_log_fixed_time)
sensitivity_anlys_post_tx_sd_and_ci_log_fixed_time <-
compute_sd_and_CI((full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_time),
log(sensitivity_anlys_event_study_data$prop_dead),
coefficient_values_sensitivity_anlys_post_tx_log_fixed_time,
p = ncol(full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_time) - 50)
sensitivity_anlys_post_tx_sd_and_ci_log_fixed_time
## lb_coef coef_values ub_coef
## (Intercept) -10.851382923 -10.702050775 -10.552718627
## StateAlaska -0.129951058 0.031180346 0.192311751
## StateArizona 0.062237502 0.200914478 0.339591454
## StateArkansas -0.652882056 -0.539628324 -0.426374592
## StateCalifornia -0.280284179 -0.142772642 -0.005261106
## StateColorado -0.173684644 -0.041235643 0.091213357
## StateConnecticut 0.045712402 0.171073189 0.296433975
## StateDelaware -0.031299986 0.096474807 0.224249599
## StateFlorida 0.292979359 0.400004719 0.507030079
## StateGeorgia 0.027723313 0.125678360 0.223633407
## StateHawaii -0.685779652 -0.546050371 -0.406321089
## StateIdaho -0.300961293 -0.191457756 -0.081954219
## StateIllinois 0.080251858 0.197690320 0.315128782
## StateIndiana -0.048730123 0.064617972 0.177966067
## StateIowa -0.740173420 -0.627597272 -0.515021123
## StateKansas -0.317384683 -0.221515850 -0.125647016
## StateKentucky 0.581068006 0.667804172 0.754540338
## StateLouisiana 0.296757848 0.391730926 0.486704004
## StateMaine -0.147659040 0.002398927 0.152456894
## StateMaryland -1.674442397 -1.476506809 -1.278571222
## StateMassachusetts -0.345097900 -0.097092247 0.150913406
## StateMichigan -0.090867966 0.002757748 0.096383462
## StateMinnesota -0.821650971 -0.713219436 -0.604787901
## StateMississippi -0.216554547 -0.112657630 -0.008760714
## StateMissouri 0.096738035 0.190079411 0.283420787
## StateMontana -0.588234827 -0.459116374 -0.329997922
## StateNebraska -1.029503669 -0.928372888 -0.827242107
## StateNevada 0.295358200 0.433982942 0.572607685
## StateNew Hampshire -0.026642612 0.092263156 0.211168925
## StateNew Jersey -0.043483622 0.103756775 0.250997172
## StateNew Mexico 0.362396333 0.539875691 0.717355049
## StateNew York -0.272977371 -0.171358842 -0.069740314
## StateNorth Carolina 0.191134194 0.271801434 0.352468675
## StateNorth Dakota -1.360528894 -1.202644720 -1.044760545
## StateOhio 0.438203925 0.565721688 0.693239451
## StateOklahoma 0.315215810 0.428514846 0.541813881
## StateOregon -0.485201765 -0.356845277 -0.228488788
## StatePennsylvania 0.555217503 0.653720080 0.752222658
## StateRhode Island -0.738417306 -0.407195727 -0.075974149
## StateSouth Carolina 0.040204678 0.134527721 0.228850765
## StateSouth Dakota -1.236760073 -1.105675466 -0.974590859
## StateTennessee 0.385612730 0.468105988 0.550599245
## StateTexas -0.037343767 0.079895079 0.197133924
## StateUtah -0.210554991 -0.064121438 0.082312116
## StateVermont -0.390574854 -0.253025999 -0.115477145
## StateVirginia -0.068149296 0.025975235 0.120099766
## StateWashington -0.152811103 -0.015154118 0.122502867
## StateWest Virginia 0.591308341 0.731595300 0.871882259
## StateWisconsin -0.036230570 0.055445595 0.147121760
## StateWyoming -0.149724782 -0.032837562 0.084049658
## factor(Time_Period_ID)2 -0.181519265 -0.003472000 0.174575265
## factor(Time_Period_ID)3 -0.055227592 0.111961355 0.279150301
## factor(Time_Period_ID)4 -0.006285391 0.163362774 0.333010938
## factor(Time_Period_ID)5 0.138220295 0.320779086 0.503337877
## factor(Time_Period_ID)6 0.161386982 0.341605096 0.521823210
## factor(Time_Period_ID)7 0.318677666 0.484414416 0.650151167
## factor(Time_Period_ID)8 0.295120454 0.468419545 0.641718637
## factor(Time_Period_ID)9 0.377703746 0.559103073 0.740502400
## factor(Time_Period_ID)10 0.379343358 0.557941170 0.736538981
## factor(Time_Period_ID)11 0.522387940 0.678363603 0.834339266
## factor(Time_Period_ID)12 0.534384149 0.698451222 0.862518296
## factor(Time_Period_ID)13 0.710228150 0.867207573 1.024186995
## factor(Time_Period_ID)14 0.763785558 0.924458344 1.085131130
## factor(Time_Period_ID)15 0.820705502 0.975279814 1.129854125
## factor(Time_Period_ID)16 0.836921733 0.993784049 1.150646366
## factor(Time_Period_ID)17 0.924687134 1.086073222 1.247459309
## factor(Time_Period_ID)18 0.931974678 1.089873139 1.247771600
## factor(Time_Period_ID)19 0.907643561 1.079776955 1.251910349
## factor(Time_Period_ID)20 0.928157249 1.090786661 1.253416073
## factor(Time_Period_ID)21 0.971986071 1.132573859 1.293161647
## factor(Time_Period_ID)22 0.941766455 1.109168843 1.276571231
## factor(Time_Period_ID)23 1.092144083 1.257961670 1.423779258
## factor(Time_Period_ID)24 1.087692787 1.258759316 1.429825845
## factor(Time_Period_ID)25 1.095278464 1.269185008 1.443091552
## factor(Time_Period_ID)26 1.099264213 1.274016826 1.448769438
## factor(Time_Period_ID)27 1.203118095 1.376344991 1.549571886
## factor(Time_Period_ID)28 1.179157165 1.353182162 1.527207160
## factor(Time_Period_ID)29 1.232904436 1.409812986 1.586721536
## factor(Time_Period_ID)30 1.250361393 1.428426147 1.606490902
## factor(Time_Period_ID)31 1.349878118 1.532155382 1.714432647
## factor(Time_Period_ID)32 1.378288200 1.563880462 1.749472724
## factor(Time_Period_ID)33 1.526709371 1.718276134 1.909842896
## factor(Time_Period_ID)34 1.546812535 1.743617576 1.940422617
## factor(Time_Period_ID)35 1.593457370 1.797158079 2.000858787
## factor(Time_Period_ID)36 1.619038318 1.822423180 2.025808043
## factor(Time_Period_ID)37 1.599423422 1.804126821 2.008830221
## factor(Time_Period_ID)38 1.579576918 1.787316007 1.995055097
## factor(Time_Period_ID)39 1.624105155 1.831885268 2.039665382
## factor(Time_Period_ID)40 1.692679976 1.900976476 2.109272976
## Naloxone_Pharmacy_Yes_Redefined -0.113010705 -0.039833456 0.033343792
## Naloxone_Pharmacy_No_Redefined -0.031499877 0.036536263 0.104572404
## Medical_Marijuana_Redefined 0.206212062 0.287444113 0.368676164
## Recreational_Marijuana_Redefined -0.349153060 -0.254884733 -0.160616406
## GSL_Redefined -0.004855940 0.052181123 0.109218186
## PDMP_Redefined -0.224291724 -0.165376426 -0.106461127
## Medicaid_Expansion_Redefined 0.036776388 0.091530614 0.146284841
## pos_0_pd -0.092104177 -0.011231024 0.069642128
## pos_1_pd -0.141291515 -0.048450678 0.044390158
## pos_2_pd -0.095192514 -0.012932139 0.069328236
## pos_3_pd -0.132796664 -0.050055638 0.032685387
## pos_4_pd -0.138199101 -0.053861337 0.030476428
## pos_5_pd -0.180273926 -0.093673112 -0.007072299
## pos_6_pd -0.195746362 -0.104939487 -0.014132613
## pos_7_pd -0.202050379 -0.104505935 -0.006961491
## pos_8_pd -0.230878959 -0.139564925 -0.048250891
## pos_9_pd -0.250068487 -0.149774196 -0.049479905
## pos_10_pd -0.272512739 -0.166228035 -0.059943332
## pos_11_pd -0.271934547 -0.175784479 -0.079634411
## pos_12_pd -0.287386696 -0.185498881 -0.083611066
## pos_13_pd -0.369647061 -0.248970121 -0.128293180
## pos_14_pd -0.358517427 -0.236851871 -0.115186314
## pos_15_pd -0.360040382 -0.237446606 -0.114852830
## pos_16_pd -0.369885963 -0.245206874 -0.120527785
## pos_17_pd -0.370887189 -0.235198785 -0.099510382
## pos_18_pd -0.336745761 -0.201208698 -0.065671634
## pos_19_pd -0.322769400 -0.197818781 -0.072868163
## pos_20_pd -0.331397159 -0.198499488 -0.065601818
## pos_21_pd -0.366555573 -0.224745881 -0.082936190
## pos_22_pd -0.375518764 -0.237067702 -0.098616639
## pos_23_pd -0.396609992 -0.254062375 -0.111514757
## pos_24_pd -0.463941799 -0.317806145 -0.171670491
## pos_25_pd -0.452525586 -0.288595851 -0.124666115
## pos_26_pd -0.444015170 -0.282744218 -0.121473266
## pos_27_pd -0.517988369 -0.334363276 -0.150738183
## pos_28_pd -0.501429011 -0.313425805 -0.125422600
## pos_29_pd -0.515880823 -0.308765586 -0.101650350
## pos_30_pd -0.486482065 -0.270213547 -0.053945029
## pos_31_pd -0.468281637 -0.225267221 0.017747195
## pos_32_pd -0.514344863 -0.271775053 -0.029205243
## pos_33_pd -0.571399730 -0.291039751 -0.010679772
## pos_34_pd -0.560213029 -0.284750791 -0.009288554
## pos_35_pd -0.698353357 -0.480443484 -0.262533611
## pos_36_pd -0.727327580 -0.519806864 -0.312286149
## pos_37_pd -0.702127892 -0.488754579 -0.275381267
## pos_38_pd -0.686398257 -0.460497592 -0.234596927
## pos_39_pd -0.828752529 -0.526170802 -0.223589075
## sd_coef
## (Intercept) 0.07618987
## StateAlaska 0.08220990
## StateArizona 0.07075356
## StateArkansas 0.05778252
## StateCalifornia 0.07015895
## StateColorado 0.06757602
## StateConnecticut 0.06395958
## StateDelaware 0.06519122
## StateFlorida 0.05460478
## StateGeorgia 0.04997706
## StateHawaii 0.07129045
## StateIdaho 0.05586915
## StateIllinois 0.05991758
## StateIndiana 0.05783066
## StateIowa 0.05743681
## StateKansas 0.04891267
## StateKentucky 0.04425315
## StateLouisiana 0.04845565
## StateMaine 0.07656019
## StateMaryland 0.10098754
## StateMassachusetts 0.12653350
## StateMichigan 0.04776822
## StateMinnesota 0.05532221
## StateMississippi 0.05300863
## StateMissouri 0.04762315
## StateMontana 0.06587676
## StateNebraska 0.05159734
## StateNevada 0.07072691
## StateNew Hampshire 0.06066621
## StateNew Jersey 0.07512265
## StateNew Mexico 0.09055069
## StateNew York 0.05184619
## StateNorth Carolina 0.04115676
## StateNorth Dakota 0.08055315
## StateOhio 0.06506008
## StateOklahoma 0.05780563
## StateOregon 0.06548800
## StatePennsylvania 0.05025642
## StateRhode Island 0.16899060
## StateSouth Carolina 0.04812400
## StateSouth Dakota 0.06687990
## StateTennessee 0.04208840
## StateTexas 0.05981574
## StateUtah 0.07471100
## StateVermont 0.07017799
## StateVirginia 0.04802272
## StateWashington 0.07023316
## StateWest Virginia 0.07157498
## StateWisconsin 0.04677355
## StateWyoming 0.05963634
## factor(Time_Period_ID)2 0.09084044
## factor(Time_Period_ID)3 0.08530048
## factor(Time_Period_ID)4 0.08655519
## factor(Time_Period_ID)5 0.09314224
## factor(Time_Period_ID)6 0.09194802
## factor(Time_Period_ID)7 0.08455957
## factor(Time_Period_ID)8 0.08841790
## factor(Time_Period_ID)9 0.09255068
## factor(Time_Period_ID)10 0.09112133
## factor(Time_Period_ID)11 0.07957942
## factor(Time_Period_ID)12 0.08370769
## factor(Time_Period_ID)13 0.08009154
## factor(Time_Period_ID)14 0.08197591
## factor(Time_Period_ID)15 0.07886444
## factor(Time_Period_ID)16 0.08003179
## factor(Time_Period_ID)17 0.08233984
## factor(Time_Period_ID)18 0.08056044
## factor(Time_Period_ID)19 0.08782316
## factor(Time_Period_ID)20 0.08297419
## factor(Time_Period_ID)21 0.08193254
## factor(Time_Period_ID)22 0.08540938
## factor(Time_Period_ID)23 0.08460081
## factor(Time_Period_ID)24 0.08727884
## factor(Time_Period_ID)25 0.08872783
## factor(Time_Period_ID)26 0.08915950
## factor(Time_Period_ID)27 0.08838107
## factor(Time_Period_ID)28 0.08878826
## factor(Time_Period_ID)29 0.09025946
## factor(Time_Period_ID)30 0.09084936
## factor(Time_Period_ID)31 0.09299860
## factor(Time_Period_ID)32 0.09468993
## factor(Time_Period_ID)33 0.09773814
## factor(Time_Period_ID)34 0.10041074
## factor(Time_Period_ID)35 0.10392893
## factor(Time_Period_ID)36 0.10376779
## factor(Time_Period_ID)37 0.10444051
## factor(Time_Period_ID)38 0.10598933
## factor(Time_Period_ID)39 0.10601026
## factor(Time_Period_ID)40 0.10627372
## Naloxone_Pharmacy_Yes_Redefined 0.03733533
## Naloxone_Pharmacy_No_Redefined 0.03471232
## Medical_Marijuana_Redefined 0.04144492
## Recreational_Marijuana_Redefined 0.04809609
## GSL_Redefined 0.02910054
## PDMP_Redefined 0.03005883
## Medicaid_Expansion_Redefined 0.02793583
## pos_0_pd 0.04126181
## pos_1_pd 0.04736777
## pos_2_pd 0.04196958
## pos_3_pd 0.04221481
## pos_4_pd 0.04302947
## pos_5_pd 0.04418409
## pos_6_pd 0.04633004
## pos_7_pd 0.04976757
## pos_8_pd 0.04658879
## pos_9_pd 0.05117056
## pos_10_pd 0.05422689
## pos_11_pd 0.04905616
## pos_12_pd 0.05198358
## pos_13_pd 0.06156987
## pos_14_pd 0.06207426
## pos_15_pd 0.06254784
## pos_16_pd 0.06361178
## pos_17_pd 0.06922878
## pos_18_pd 0.06915156
## pos_19_pd 0.06375032
## pos_20_pd 0.06780493
## pos_21_pd 0.07235188
## pos_22_pd 0.07063830
## pos_23_pd 0.07272838
## pos_24_pd 0.07455901
## pos_25_pd 0.08363762
## pos_26_pd 0.08228110
## pos_27_pd 0.09368627
## pos_28_pd 0.09592000
## pos_29_pd 0.10567104
## pos_30_pd 0.11034108
## pos_31_pd 0.12398695
## pos_32_pd 0.12376011
## pos_33_pd 0.14304081
## pos_34_pd 0.14054196
## pos_35_pd 0.11117851
## pos_36_pd 0.10587792
## pos_37_pd 0.10886393
## pos_38_pd 0.11525544
## pos_39_pd 0.15437843
Plot Results
#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx_log_fixed_time <- sensitivity_anlys_post_tx_sd_and_ci_log_fixed_time %>%
mutate(term = rownames(sensitivity_anlys_post_tx_sd_and_ci_log_fixed_time)) %>%
dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
filter(term %in% c(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_post_tx_log_fixed_time) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx_log_fixed_time$num_states <- sapply(plot_post_tx_log_fixed_time$term, function(x){sum(sensitivity_anlys_event_study_data[,x])})
dwplot(plot_post_tx_log_fixed_time, colour = "black",
vars_order = c(sapply(((max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0),
function(x){paste("pos_", x, "_pd", sep = "")}))) +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black"),
axis.text.x = element_text(angle = 45, size = 4)) +
geom_vline(aes(xintercept = 0), linetype = "dashed") +
labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals",
title = "Coefficient of Pre-Intervention and Post-Intervention Periods") +
scale_color_grey() +
coord_flip() +
geom_vline(aes(xintercept = coef(main_analysis_model_log_fixed_time)["Intervention_Redefined"]), linetype = "dashed", color = "red") +
geom_text(aes(label = paste("Coefficient Estimate: ", coef(main_analysis_model_log_fixed_time)["Intervention_Redefined"]), y = 12,
x = coef(main_analysis_model_log_fixed_time)["Intervention_Redefined"] + 0.1), color = "red")
# geom_text(aes(label = num_states, x = .1, y = 40:1), size = 2)
OLS Model Main Analysis With Linear Fixed Time Effects Interacted with Region With Log Proportion
#compute the proportion of people who died from drug overdose
main_analysis_data$prop_dead <- main_analysis_data$imputed_deaths/main_analysis_data$population
#fit an OLS with smoothed time effects
main_analysis_model_log_fixed_lin_time<-lm(log(prop_dead)~ State +
Time_Period_ID:Region +
I(Time_Period_ID^2):Region +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +
Intervention_Redefined ,
data = main_analysis_data)
summary(main_analysis_model_log_fixed_lin_time)
##
## Call:
## lm(formula = log(prop_dead) ~ State + Time_Period_ID:Region +
## I(Time_Period_ID^2):Region + Naloxone_Pharmacy_Yes_Redefined +
## Naloxone_Pharmacy_No_Redefined + Medical_Marijuana_Redefined +
## Recreational_Marijuana_Redefined + GSL_Redefined + PDMP_Redefined +
## Medicaid_Expansion_Redefined + Intervention_Redefined, data = main_analysis_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.11885 -0.14274 0.01294 0.16151 1.08925
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.077e+01 5.984e-02 -180.045 < 2e-16 ***
## StateAlaska 3.765e-01 9.020e-02 4.174 3.13e-05 ***
## StateArizona 5.260e-01 8.687e-02 6.055 1.69e-09 ***
## StateArkansas -4.947e-01 6.844e-02 -7.228 7.02e-13 ***
## StateCalifornia 6.715e-02 9.010e-02 0.745 0.456170
## StateColorado 2.472e-01 9.004e-02 2.745 0.006106 **
## StateConnecticut 9.452e-02 9.118e-02 1.037 0.300018
## StateDelaware 1.911e-01 6.967e-02 2.743 0.006149 **
## StateFlorida 3.201e-01 6.849e-02 4.674 3.15e-06 ***
## StateGeorgia 7.540e-04 6.848e-02 0.011 0.991216
## StateHawaii -1.573e-01 9.011e-02 -1.746 0.080971 .
## StateIdaho 1.127e-01 8.783e-02 1.283 0.199685
## StateIllinois 1.101e-02 8.772e-02 0.126 0.900137
## StateIndiana -3.875e-02 8.750e-02 -0.443 0.657902
## StateIowa -7.871e-01 8.696e-02 -9.052 < 2e-16 ***
## StateKansas -3.434e-01 8.680e-02 -3.957 7.87e-05 ***
## StateKentucky 6.920e-01 6.845e-02 10.109 < 2e-16 ***
## StateLouisiana 3.491e-01 6.767e-02 5.159 2.73e-07 ***
## StateMaine -6.228e-02 9.377e-02 -0.664 0.506700
## StateMaryland -1.509e+00 6.945e-02 -21.732 < 2e-16 ***
## StateMassachusetts -2.204e-01 9.110e-02 -2.420 0.015632 *
## StateMichigan -1.065e-01 8.789e-02 -1.212 0.225640
## StateMinnesota -7.849e-01 8.880e-02 -8.838 < 2e-16 ***
## StateMississippi -5.743e-02 6.772e-02 -0.848 0.396496
## StateMissouri 4.478e-02 8.831e-02 0.507 0.612120
## StateMontana -1.949e-01 8.772e-02 -2.222 0.026399 *
## StateNebraska -9.822e-01 8.789e-02 -11.175 < 2e-16 ***
## StateNevada 6.930e-01 8.880e-02 7.804 9.72e-15 ***
## StateNew Hampshire 1.089e-02 9.090e-02 0.120 0.904628
## StateNew Jersey -5.519e-02 9.043e-02 -0.610 0.541703
## StateNew Mexico 8.623e-01 8.919e-02 9.668 < 2e-16 ***
## StateNew York -2.743e-01 9.079e-02 -3.022 0.002547 **
## StateNorth Carolina 2.243e-01 6.753e-02 3.321 0.000915 ***
## StateNorth Dakota -1.267e+00 8.728e-02 -14.511 < 2e-16 ***
## StateOhio 3.399e-01 8.691e-02 3.911 9.52e-05 ***
## StateOklahoma 4.557e-01 6.816e-02 6.686 2.98e-11 ***
## StateOregon -6.969e-02 8.992e-02 -0.775 0.438394
## StatePennsylvania 4.449e-01 9.126e-02 4.875 1.18e-06 ***
## StateRhode Island -4.293e-01 9.162e-02 -4.686 2.98e-06 ***
## StateSouth Carolina 2.013e-01 6.809e-02 2.957 0.003148 **
## StateSouth Dakota -1.160e+00 8.796e-02 -13.187 < 2e-16 ***
## StateTennessee 4.640e-01 6.738e-02 6.887 7.67e-12 ***
## StateTexas -6.816e-03 6.842e-02 -0.100 0.920656
## StateUtah 1.602e-01 8.655e-02 1.851 0.064293 .
## StateVermont -3.249e-01 9.116e-02 -3.564 0.000374 ***
## StateVirginia -2.543e-02 6.768e-02 -0.376 0.707139
## StateWashington 2.596e-01 9.036e-02 2.873 0.004115 **
## StateWest Virginia 7.942e-01 6.850e-02 11.595 < 2e-16 ***
## StateWisconsin -1.123e-01 8.698e-02 -1.291 0.197017
## StateWyoming 2.347e-01 8.695e-02 2.699 0.007005 **
## Naloxone_Pharmacy_Yes_Redefined 5.414e-02 3.941e-02 1.374 0.169687
## Naloxone_Pharmacy_No_Redefined 1.445e-02 3.883e-02 0.372 0.709784
## Medical_Marijuana_Redefined 2.141e-01 3.118e-02 6.868 8.73e-12 ***
## Recreational_Marijuana_Redefined -8.103e-02 4.907e-02 -1.651 0.098804 .
## GSL_Redefined 4.745e-02 3.175e-02 1.495 0.135166
## PDMP_Redefined -1.653e-01 2.496e-02 -6.623 4.55e-11 ***
## Medicaid_Expansion_Redefined 7.859e-02 3.003e-02 2.617 0.008939 **
## Intervention_Redefined -5.397e-02 2.454e-02 -2.199 0.027986 *
## Time_Period_ID:RegionMidwest 8.179e-02 5.292e-03 15.456 < 2e-16 ***
## Time_Period_ID:RegionNortheast 7.251e-02 6.096e-03 11.896 < 2e-16 ***
## Time_Period_ID:RegionSouth 7.480e-02 4.671e-03 16.015 < 2e-16 ***
## Time_Period_ID:RegionWest 6.411e-02 5.191e-03 12.349 < 2e-16 ***
## RegionMidwest:I(Time_Period_ID^2) -8.933e-04 1.294e-04 -6.901 6.98e-12 ***
## RegionNortheast:I(Time_Period_ID^2) -5.466e-04 1.495e-04 -3.657 0.000262 ***
## RegionSouth:I(Time_Period_ID^2) -8.581e-04 1.189e-04 -7.217 7.61e-13 ***
## RegionWest:I(Time_Period_ID^2) -9.039e-04 1.305e-04 -6.927 5.83e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3009 on 1934 degrees of freedom
## Multiple R-squared: 0.8371, Adjusted R-squared: 0.8316
## F-statistic: 152.9 on 65 and 1934 DF, p-value: < 2.2e-16
#examine fitted values
summary(fitted(main_analysis_model_log_fixed_lin_time))
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -12.209 -10.218 -9.750 -9.796 -9.329 -8.127
hist(fitted(main_analysis_model_log_fixed_lin_time))
par(mfrow = c(2,2))
plot(main_analysis_model_log_fixed_lin_time)
Coefficients and 95% CI
#compute the full dataset including basis functions
full_df_w_basis_functions_log_fixed_lin_time <- model.matrix(main_analysis_model_log_fixed_lin_time)
#estimate the 95% CI and SD
coefficient_values_log_fixed_lin_time <- coef(main_analysis_model_log_fixed_lin_time)
#type = "response" to get the estimated probabilities
main_analysis_sd_and_ci_log_fixed_lin_time <- compute_sd_and_CI(full_df_w_basis_functions_log_fixed_lin_time,
log(main_analysis_data$prop_dead),
coefficient_values_log_fixed_lin_time,
p = ncol(full_df_w_basis_functions_log_fixed_lin_time) - 50)
main_analysis_sd_and_ci_log_fixed_lin_time
## lb_coef coef_values ub_coef
## (Intercept) -10.870532086 -1.077330e+01 -1.067607e+01
## StateAlaska 0.227816678 3.764610e-01 5.251054e-01
## StateArizona 0.390612117 5.259709e-01 6.613297e-01
## StateArkansas -0.604794078 -4.946764e-01 -3.845586e-01
## StateCalifornia -0.089434784 6.715414e-02 2.237431e-01
## StateColorado 0.108661454 2.471601e-01 3.856588e-01
## StateConnecticut -0.144557560 9.452006e-02 3.335977e-01
## StateDelaware 0.067867770 1.910826e-01 3.142975e-01
## StateFlorida 0.213681393 3.201422e-01 4.266031e-01
## StateGeorgia -0.086244949 7.539808e-04 8.775291e-02
## StateHawaii -0.302406580 -1.573225e-01 -1.223844e-02
## StateIdaho -0.028208915 1.126758e-01 2.535605e-01
## StateIllinois -0.161293636 1.100985e-02 1.833133e-01
## StateIndiana -0.190069700 -3.875005e-02 1.125696e-01
## StateIowa -0.922491125 -7.871038e-01 -6.517165e-01
## StateKansas -0.476952541 -3.434288e-01 -2.099050e-01
## StateKentucky 0.605308589 6.919793e-01 7.786499e-01
## StateLouisiana 0.250558266 3.491381e-01 4.477179e-01
## StateMaine -0.307386749 -6.227663e-02 1.828335e-01
## StateMaryland -1.708316110 -1.509208e+00 -1.310100e+00
## StateMassachusetts -0.561705395 -2.204241e-01 1.208572e-01
## StateMichigan -0.239268393 -1.065315e-01 2.620537e-02
## StateMinnesota -0.923565633 -7.848809e-01 -6.461961e-01
## StateMississippi -0.152855044 -5.743181e-02 3.799143e-02
## StateMissouri -0.085733292 4.478408e-02 1.753014e-01
## StateMontana -0.336215945 -1.949090e-01 -5.360210e-02
## StateNebraska -1.113111783 -9.821615e-01 -8.512112e-01
## StateNevada 0.547851351 6.929982e-01 8.381450e-01
## StateNew Hampshire -0.220119819 1.089307e-02 2.419060e-01
## StateNew Jersey -0.309227369 -5.519172e-02 1.988439e-01
## StateNew Mexico 0.703870882 8.622936e-01 1.020716e+00
## StateNew York -0.505083199 -2.743314e-01 -4.357956e-02
## StateNorth Carolina 0.136280670 2.242541e-01 3.122274e-01
## StateNorth Dakota -1.442024087 -1.266542e+00 -1.091059e+00
## StateOhio 0.204411181 3.398957e-01 4.753802e-01
## StateOklahoma 0.345493483 4.557456e-01 5.659976e-01
## StateOregon -0.209913729 -6.969390e-02 7.052594e-02
## StatePennsylvania 0.222212940 4.448805e-01 6.675480e-01
## StateRhode Island -0.837302163 -4.292993e-01 -2.129647e-02
## StateSouth Carolina 0.111509198 2.013118e-01 2.911145e-01
## StateSouth Dakota -1.317921300 -1.159922e+00 -1.001924e+00
## StateTennessee 0.379504435 4.640316e-01 5.485588e-01
## StateTexas -0.121362607 -6.816327e-03 1.077300e-01
## StateUtah -0.043845600 1.602299e-01 3.643053e-01
## StateVermont -0.572803061 -3.249195e-01 -7.703584e-02
## StateVirginia -0.122942397 -2.542955e-02 7.208329e-02
## StateWashington 0.117677605 2.595663e-01 4.014550e-01
## StateWest Virginia 0.652987520 7.942308e-01 9.354740e-01
## StateWisconsin -0.237211780 -1.122536e-01 1.270455e-02
## StateWyoming 0.067986094 2.347091e-01 4.014321e-01
## Naloxone_Pharmacy_Yes_Redefined -0.009128978 5.413660e-02 1.174022e-01
## Naloxone_Pharmacy_No_Redefined -0.047020174 1.445200e-02 7.592417e-02
## Medical_Marijuana_Redefined 0.145383479 2.141197e-01 2.828558e-01
## Recreational_Marijuana_Redefined -0.155713354 -8.103395e-02 -6.354555e-03
## GSL_Redefined -0.005849108 4.745038e-02 1.007499e-01
## PDMP_Redefined -0.218050934 -1.652800e-01 -1.125091e-01
## Medicaid_Expansion_Redefined 0.028563796 7.859406e-02 1.286243e-01
## Intervention_Redefined -0.099588037 -5.397472e-02 -8.361396e-03
## Time_Period_ID:RegionMidwest 0.072485767 8.178652e-02 9.108728e-02
## Time_Period_ID:RegionNortheast 0.050914470 7.251276e-02 9.411106e-02
## Time_Period_ID:RegionSouth 0.066136530 7.480447e-02 8.347241e-02
## Time_Period_ID:RegionWest 0.054947367 6.410565e-02 7.326393e-02
## RegionMidwest:I(Time_Period_ID^2) -0.001107586 -8.933230e-04 -6.790600e-04
## RegionNortheast:I(Time_Period_ID^2) -0.001003649 -5.465679e-04 -8.948637e-05
## RegionSouth:I(Time_Period_ID^2) -0.001078072 -8.581239e-04 -6.381757e-04
## RegionWest:I(Time_Period_ID^2) -0.001120720 -9.038570e-04 -6.869936e-04
## sd_coef
## (Intercept) 0.0496071198
## StateAlaska 0.0758389536
## StateArizona 0.0690606190
## StateArkansas 0.0561825087
## StateCalifornia 0.0798923104
## StateColorado 0.0706625829
## StateConnecticut 0.1219783755
## StateDelaware 0.0628647209
## StateFlorida 0.0543167495
## StateGeorgia 0.0443872093
## StateHawaii 0.0740224857
## StateIdaho 0.0718799472
## StateIllinois 0.0879099441
## StateIndiana 0.0772039012
## StateIowa 0.0690751589
## StateKansas 0.0681243626
## StateKentucky 0.0442197305
## StateLouisiana 0.0502958363
## StateMaine 0.1250561821
## StateMaryland 0.1015857987
## StateMassachusetts 0.1741231035
## StateMichigan 0.0677228979
## StateMinnesota 0.0707575372
## StateMississippi 0.0486853239
## StateMissouri 0.0665904937
## StateMontana 0.0720953687
## StateNebraska 0.0668113767
## StateNevada 0.0740545048
## StateNew Hampshire 0.1178637172
## StateNew Jersey 0.1296100240
## StateNew Mexico 0.0808279105
## StateNew York 0.1177305210
## StateNorth Carolina 0.0448843790
## StateNorth Dakota 0.0895317936
## StateOhio 0.0691247462
## StateOklahoma 0.0562510604
## StateOregon 0.0715407308
## StatePennsylvania 0.1136058778
## StateRhode Island 0.2081647169
## StateSouth Carolina 0.0458176666
## StateSouth Dakota 0.0806116835
## StateTennessee 0.0431261187
## StateTexas 0.0584419796
## StateUtah 0.1041201296
## StateVermont 0.1264712293
## StateVirginia 0.0497514504
## StateWashington 0.0723921994
## StateWest Virginia 0.0720628801
## StateWisconsin 0.0637541664
## StateWyoming 0.0850627595
## Naloxone_Pharmacy_Yes_Redefined 0.0322783540
## Naloxone_Pharmacy_No_Redefined 0.0313633541
## Medical_Marijuana_Redefined 0.0350694817
## Recreational_Marijuana_Redefined 0.0381017345
## GSL_Redefined 0.0271936176
## PDMP_Redefined 0.0269239364
## Medicaid_Expansion_Redefined 0.0255256427
## Intervention_Redefined 0.0232721023
## Time_Period_ID:RegionMidwest 0.0047452848
## Time_Period_ID:RegionNortheast 0.0110195384
## Time_Period_ID:RegionSouth 0.0044224191
## Time_Period_ID:RegionWest 0.0046725918
## RegionMidwest:I(Time_Period_ID^2) 0.0001093179
## RegionNortheast:I(Time_Period_ID^2) 0.0002332049
## RegionSouth:I(Time_Period_ID^2) 0.0001122185
## RegionWest:I(Time_Period_ID^2) 0.0001106446
Attributable Deaths
date_data <- main_analysis_data[, c("Time_Period_ID", "Time_Period_Start")]
date_data <- date_data[!duplicated(date_data),]
attr_deaths_est_log_lin_time <- attr_death_compute(main_analysis_data,
main_analysis_sd_and_ci_log_fixed_lin_time,
post_tx_model = FALSE, tx_name = "Intervention_Redefined")
attr_deaths_est_log_lin_time <- merge(attr_deaths_est_log_lin_time, date_data,
by.x = "Time_Period", by.y = "Time_Period_ID")
ggplot(attr_deaths_est_log_lin_time, aes(x = Time_Period_Start)) +
# geom_point(aes(y = attr_deaths)) +
geom_line(aes(y = attr_deaths, linetype = "Estimate")) +
# geom_point(aes(y = attr_deaths_lb)) +
geom_line(aes(y = attr_deaths_lb, linetype = "95% CI")) +
# geom_point(aes(y = attr_deaths_ub)) +
geom_line(aes(y = attr_deaths_ub, linetype = "95% CI")) +
labs(x = "Date", y = "Attributable Deaths",
title = "Estimated Number of Attributable Deaths Using Linear and Quad. Time Effects,
Log Probability of Drug Overdose Death",
linetype = "") +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black")) +
scale_linetype_manual(values = c("dashed", "solid"))
Linear Policy Measures
#use this function to compute the cumulative sum, but resets the sum if the variable was 0
compute_cumsum = function(x){
cs = cumsum(x)
cs - cummax((x == 0) * cs)
}
sensitivity_anlys_event_study_data_lin_post_tx <- sensitivity_anlys_event_study_data %>%
arrange(State, Time_Period_ID) %>%
group_by(State) %>%
mutate(sum_tx_periods = pos_0_pd + pos_1_pd + pos_2_pd + pos_3_pd +
pos_4_pd + pos_5_pd + pos_6_pd + pos_7_pd + pos_8_pd + pos_9_pd +
pos_10_pd + pos_11_pd + pos_12_pd + pos_13_pd + pos_14_pd +
pos_15_pd + pos_16_pd + pos_17_pd + pos_18_pd + pos_19_pd +
pos_20_pd + pos_21_pd + pos_22_pd + pos_23_pd + pos_24_pd +
pos_25_pd + pos_26_pd + pos_27_pd + pos_28_pd + pos_29_pd +
pos_30_pd + pos_31_pd + pos_32_pd + pos_33_pd + pos_34_pd +
pos_35_pd + pos_36_pd + pos_37_pd + pos_38_pd + pos_39_pd,
time_after_tx = compute_cumsum(sum_tx_periods),
num_pd_w_tx = compute_cumsum(Intervention_Redefined),
num_pd_w_naloxone_yes = compute_cumsum(Naloxone_Pharmacy_Yes_Redefined),
num_pd_w_naloxone_no = compute_cumsum(Naloxone_Pharmacy_No_Redefined),
num_pd_w_med_marijuana = compute_cumsum(Medical_Marijuana_Redefined),
num_pd_w_rec_marijuana = compute_cumsum(Recreational_Marijuana_Redefined),
num_pd_w_gsl = compute_cumsum(GSL_Redefined),
num_pd_w_pdmp = compute_cumsum(PDMP_Redefined),
num_pd_w_medicaid = compute_cumsum(Medicaid_Expansion_Redefined),
lag_num_pd_w_tx = lag(num_pd_w_tx))
sensitivity_anlys_event_study_data_lin_post_tx$lag_num_pd_w_tx[is.na(sensitivity_anlys_event_study_data_lin_post_tx$lag_num_pd_w_tx)] <- 0
#run the gam model
sensitivity_anlys_lin_post_tx_model_linear_time<-lm(log(prop_dead)~ State +
Time_Period_ID:Region +
I(Time_Period_ID^2):Region +
num_pd_w_naloxone_yes +
num_pd_w_naloxone_no +
num_pd_w_med_marijuana +
num_pd_w_rec_marijuana +
num_pd_w_gsl +
num_pd_w_pdmp +
num_pd_w_medicaid +
Intervention_Redefined+
lag_num_pd_w_tx,
data = sensitivity_anlys_event_study_data_lin_post_tx)
summary(sensitivity_anlys_lin_post_tx_model_linear_time)
##
## Call:
## lm(formula = log(prop_dead) ~ State + Time_Period_ID:Region +
## I(Time_Period_ID^2):Region + num_pd_w_naloxone_yes + num_pd_w_naloxone_no +
## num_pd_w_med_marijuana + num_pd_w_rec_marijuana + num_pd_w_gsl +
## num_pd_w_pdmp + num_pd_w_medicaid + Intervention_Redefined +
## lag_num_pd_w_tx, data = sensitivity_anlys_event_study_data_lin_post_tx)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.22313 -0.13603 0.01109 0.15412 1.09172
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.081e+01 5.983e-02 -180.708 < 2e-16 ***
## StateAlaska 5.265e-01 8.961e-02 5.876 4.95e-09 ***
## StateArizona 4.732e-01 9.036e-02 5.237 1.81e-07 ***
## StateArkansas -4.311e-01 6.966e-02 -6.189 7.38e-10 ***
## StateCalifornia 3.097e-01 9.223e-02 3.358 0.000800 ***
## StateColorado 4.190e-01 8.859e-02 4.729 2.42e-06 ***
## StateConnecticut 3.481e-02 9.355e-02 0.372 0.709872
## StateDelaware 2.790e-01 7.059e-02 3.952 8.04e-05 ***
## StateFlorida 5.838e-01 7.199e-02 8.110 8.91e-16 ***
## StateGeorgia 3.100e-01 7.384e-02 4.199 2.80e-05 ***
## StateHawaii -1.777e-01 9.066e-02 -1.960 0.050118 .
## StateIdaho -2.427e-01 9.291e-02 -2.612 0.009070 **
## StateIllinois 2.272e-02 9.231e-02 0.246 0.805600
## StateIndiana -2.942e-01 9.057e-02 -3.249 0.001179 **
## StateIowa -7.920e-01 8.697e-02 -9.107 < 2e-16 ***
## StateKansas -3.569e-01 8.635e-02 -4.133 3.74e-05 ***
## StateKentucky 5.010e-01 7.098e-02 7.059 2.34e-12 ***
## StateLouisiana 4.570e-01 6.807e-02 6.714 2.49e-11 ***
## StateMaine 1.134e-01 9.586e-02 1.183 0.237057
## StateMaryland -1.259e+00 7.266e-02 -17.334 < 2e-16 ***
## StateMassachusetts -4.600e-01 9.202e-02 -4.998 6.31e-07 ***
## StateMichigan -9.613e-02 9.093e-02 -1.057 0.290537
## StateMinnesota -6.145e-01 8.934e-02 -6.879 8.11e-12 ***
## StateMississippi -1.524e-01 6.811e-02 -2.237 0.025377 *
## StateMissouri 2.503e-01 8.865e-02 2.824 0.004795 **
## StateMontana 1.278e-01 9.014e-02 1.418 0.156450
## StateNebraska -1.018e+00 8.815e-02 -11.544 < 2e-16 ***
## StateNevada 8.067e-01 8.896e-02 9.067 < 2e-16 ***
## StateNew Hampshire -1.251e-02 9.376e-02 -0.133 0.893884
## StateNew Jersey 1.547e-02 9.339e-02 0.166 0.868419
## StateNew Mexico 8.940e-01 9.177e-02 9.741 < 2e-16 ***
## StateNew York -4.983e-01 9.161e-02 -5.439 6.04e-08 ***
## StateNorth Carolina 2.940e-01 6.775e-02 4.339 1.50e-05 ***
## StateNorth Dakota -1.392e+00 8.757e-02 -15.891 < 2e-16 ***
## StateOhio 4.864e-01 8.964e-02 5.426 6.48e-08 ***
## StateOklahoma 3.140e-01 7.060e-02 4.448 9.16e-06 ***
## StateOregon 2.450e-01 8.915e-02 2.748 0.006048 **
## StatePennsylvania 3.417e-01 9.446e-02 3.617 0.000305 ***
## StateRhode Island -5.881e-01 9.285e-02 -6.334 2.96e-10 ***
## StateSouth Carolina 1.258e-01 6.874e-02 1.830 0.067393 .
## StateSouth Dakota -1.251e+00 8.884e-02 -14.080 < 2e-16 ***
## StateTennessee 4.218e-01 6.737e-02 6.261 4.69e-10 ***
## StateTexas 3.528e-02 7.309e-02 0.483 0.629342
## StateUtah -4.513e-02 9.206e-02 -0.490 0.624001
## StateVermont -2.578e-01 9.103e-02 -2.832 0.004671 **
## StateVirginia 1.442e-02 6.906e-02 0.209 0.834616
## StateWashington 4.951e-01 8.928e-02 5.546 3.33e-08 ***
## StateWest Virginia 6.012e-01 7.160e-02 8.397 < 2e-16 ***
## StateWisconsin -2.082e-02 8.706e-02 -0.239 0.811027
## StateWyoming 1.606e-02 9.063e-02 0.177 0.859364
## num_pd_w_naloxone_yes -7.162e-03 5.598e-03 -1.279 0.200931
## num_pd_w_naloxone_no -1.361e-02 3.652e-03 -3.727 0.000200 ***
## num_pd_w_med_marijuana -9.307e-03 2.199e-03 -4.233 2.41e-05 ***
## num_pd_w_rec_marijuana -2.385e-02 8.065e-03 -2.957 0.003144 **
## num_pd_w_gsl 1.578e-02 3.819e-03 4.133 3.74e-05 ***
## num_pd_w_pdmp 8.359e-03 2.272e-03 3.679 0.000240 ***
## num_pd_w_medicaid 2.492e-02 4.310e-03 5.781 8.64e-09 ***
## Intervention_Redefined -7.822e-02 2.481e-02 -3.153 0.001643 **
## lag_num_pd_w_tx -1.528e-02 1.851e-03 -8.255 2.77e-16 ***
## Time_Period_ID:RegionMidwest 7.835e-02 5.207e-03 15.049 < 2e-16 ***
## Time_Period_ID:RegionNortheast 7.695e-02 6.247e-03 12.317 < 2e-16 ***
## Time_Period_ID:RegionSouth 6.482e-02 4.704e-03 13.779 < 2e-16 ***
## Time_Period_ID:RegionWest 6.953e-02 5.575e-03 12.472 < 2e-16 ***
## RegionMidwest:I(Time_Period_ID^2) -7.113e-04 1.317e-04 -5.401 7.46e-08 ***
## RegionNortheast:I(Time_Period_ID^2) -4.616e-04 1.578e-04 -2.925 0.003483 **
## RegionSouth:I(Time_Period_ID^2) -5.745e-04 1.242e-04 -4.626 3.97e-06 ***
## RegionWest:I(Time_Period_ID^2) -9.302e-04 1.360e-04 -6.842 1.05e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2987 on 1933 degrees of freedom
## Multiple R-squared: 0.8395, Adjusted R-squared: 0.8341
## F-statistic: 153.2 on 66 and 1933 DF, p-value: < 2.2e-16
Sandwich Estimator
#compute the full dataset including basis functions
full_df_w_basis_functions_log_fixed_lin_time_lin_post_tx <- model.matrix(sensitivity_anlys_lin_post_tx_model_linear_time)
#estimate the 95% CI and SD
coefficient_values_log_fixed_lin_time_lin_post_tx <- coef(sensitivity_anlys_lin_post_tx_model_linear_time)
#type = "response" to get the estimated probabilities
main_analysis_sd_and_ci_log_fixed_lin_time_lin_post_tx <- compute_sd_and_CI(full_df_w_basis_functions_log_fixed_lin_time_lin_post_tx,
log(sensitivity_anlys_event_study_data_lin_post_tx$prop_dead),
coefficient_values_log_fixed_lin_time_lin_post_tx,
p = ncol(full_df_w_basis_functions_log_fixed_lin_time_lin_post_tx) - 50)
round(main_analysis_sd_and_ci_log_fixed_lin_time_lin_post_tx,4)
## lb_coef coef_values ub_coef sd_coef
## (Intercept) -10.8971 -10.8119 -10.7267 0.0435
## StateAlaska 0.3782 0.5265 0.6749 0.0757
## StateArizona 0.3236 0.4732 0.6229 0.0764
## StateArkansas -0.5372 -0.4311 -0.3250 0.0541
## StateCalifornia 0.1508 0.3097 0.4686 0.0811
## StateColorado 0.2997 0.4190 0.5382 0.0609
## StateConnecticut -0.2137 0.0348 0.2833 0.1268
## StateDelaware 0.1722 0.2790 0.3857 0.0544
## StateFlorida 0.4703 0.5838 0.6974 0.0580
## StateGeorgia 0.2049 0.3100 0.4152 0.0537
## StateHawaii -0.3154 -0.1777 -0.0400 0.0703
## StateIdaho -0.4075 -0.2427 -0.0779 0.0841
## StateIllinois -0.1358 0.0227 0.1813 0.0809
## StateIndiana -0.4417 -0.2942 -0.1467 0.0753
## StateIowa -0.9155 -0.7920 -0.6684 0.0630
## StateKansas -0.4841 -0.3569 -0.2297 0.0649
## StateKentucky 0.4072 0.5010 0.5949 0.0479
## StateLouisiana 0.3600 0.4570 0.5539 0.0495
## StateMaine -0.1363 0.1134 0.3630 0.1274
## StateMaryland -1.4542 -1.2595 -1.0647 0.0994
## StateMassachusetts -0.8118 -0.4600 -0.1081 0.1795
## StateMichigan -0.2281 -0.0961 0.0358 0.0673
## StateMinnesota -0.7400 -0.6145 -0.4891 0.0640
## StateMississippi -0.2577 -0.1524 -0.0471 0.0537
## StateMissouri 0.1236 0.2503 0.3771 0.0647
## StateMontana -0.0338 0.1278 0.2893 0.0824
## StateNebraska -1.1396 -1.0176 -0.8955 0.0623
## StateNevada 0.6796 0.8067 0.9337 0.0648
## StateNew Hampshire -0.2309 -0.0125 0.2059 0.1114
## StateNew Jersey -0.2259 0.0155 0.2569 0.1232
## StateNew Mexico 0.7175 0.8940 1.0705 0.0901
## StateNew York -0.7476 -0.4983 -0.2490 0.1272
## StateNorth Carolina 0.2159 0.2940 0.3720 0.0398
## StateNorth Dakota -1.5705 -1.3916 -1.2127 0.0913
## StateOhio 0.3467 0.4864 0.6261 0.0713
## StateOklahoma 0.2124 0.3140 0.4157 0.0519
## StateOregon 0.1198 0.2450 0.3702 0.0639
## StatePennsylvania 0.1129 0.3417 0.5705 0.1167
## StateRhode Island -1.0350 -0.5881 -0.1413 0.2280
## StateSouth Carolina 0.0338 0.1258 0.2178 0.0469
## StateSouth Dakota -1.4037 -1.2508 -1.0979 0.0780
## StateTennessee 0.3499 0.4218 0.4938 0.0367
## StateTexas -0.0672 0.0353 0.1378 0.0523
## StateUtah -0.2766 -0.0451 0.1863 0.1181
## StateVermont -0.4935 -0.2578 -0.0222 0.1202
## StateVirginia -0.0759 0.0144 0.1048 0.0461
## StateWashington 0.3654 0.4951 0.6248 0.0662
## StateWest Virginia 0.4548 0.6012 0.7476 0.0747
## StateWisconsin -0.1383 -0.0208 0.0966 0.0599
## StateWyoming -0.1504 0.0161 0.1825 0.0849
## num_pd_w_naloxone_yes -0.0174 -0.0072 0.0031 0.0052
## num_pd_w_naloxone_no -0.0200 -0.0136 -0.0073 0.0032
## num_pd_w_med_marijuana -0.0144 -0.0093 -0.0042 0.0026
## num_pd_w_rec_marijuana -0.0360 -0.0238 -0.0117 0.0062
## num_pd_w_gsl 0.0073 0.0158 0.0243 0.0043
## num_pd_w_pdmp 0.0035 0.0084 0.0132 0.0025
## num_pd_w_medicaid 0.0172 0.0249 0.0326 0.0039
## Intervention_Redefined -0.1254 -0.0782 -0.0310 0.0241
## lag_num_pd_w_tx -0.0193 -0.0153 -0.0113 0.0020
## Time_Period_ID:RegionMidwest 0.0694 0.0784 0.0873 0.0045
## Time_Period_ID:RegionNortheast 0.0556 0.0769 0.0983 0.0109
## Time_Period_ID:RegionSouth 0.0572 0.0648 0.0724 0.0039
## Time_Period_ID:RegionWest 0.0587 0.0695 0.0804 0.0055
## RegionMidwest:I(Time_Period_ID^2) -0.0009 -0.0007 -0.0005 0.0001
## RegionNortheast:I(Time_Period_ID^2) -0.0009 -0.0005 0.0000 0.0002
## RegionSouth:I(Time_Period_ID^2) -0.0008 -0.0006 -0.0004 0.0001
## RegionWest:I(Time_Period_ID^2) -0.0012 -0.0009 -0.0007 0.0001
Attributable Deaths
date_data <- main_analysis_data[, c("Time_Period_ID", "Time_Period_Start")]
date_data <- date_data[!duplicated(date_data),]
attr_deaths_est_log_lin_time_lin_post_tx <- attr_death_compute(sensitivity_anlys_event_study_data_lin_post_tx,
main_analysis_sd_and_ci_log_fixed_lin_time_lin_post_tx,
post_tx_model = FALSE, tx_name = "num_pd_w_tx")
attr_deaths_est_log_lin_time_lin_post_tx <- merge(attr_deaths_est_log_lin_time_lin_post_tx, date_data,
by.x = "Time_Period", by.y = "Time_Period_ID")
ggplot(attr_deaths_est_log_lin_time_lin_post_tx, aes(x = Time_Period_Start)) +
# geom_point(aes(y = attr_deaths)) +
geom_line(aes(y = attr_deaths, linetype = "Estimate")) +
# geom_point(aes(y = attr_deaths_lb)) +
geom_line(aes(y = attr_deaths_lb, linetype = "95% CI")) +
# geom_point(aes(y = attr_deaths_ub)) +
geom_line(aes(y = attr_deaths_ub, linetype = "95% CI")) +
labs(x = "Date", y = "Attributable Deaths",
title = "Estimated Number of Attributable Deaths Using Linear and Quad. Time Effects,
Log Probability of Drug Overdose Death, Linear Policy Effects",
linetype = "") +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black")) +
scale_linetype_manual(values = c("dashed", "solid"))
Event Study
Model Fitting
#create a formula for the gam model which includes the state effects, smoothed time effects, policy measures,
#the periods before the intervention (excluding 1 period and 34 periods before intervention)
#the intervention period, and the periods after the intervention
formula_event_study_log_fixed_lin_time <- formula(paste("log(prop_dead) ~ State +
Time_Period_ID:Region +
I(Time_Period_ID^2):Region +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +",
paste(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)-2),
function(x)paste("neg_", x, "_pd", sep = "")), collapse = "+"),
"+",
paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_event_study_model_log_fixed_lin_time<-lm(formula_event_study_log_fixed_lin_time,
data = sensitivity_anlys_event_study_data)
summary(sensitivity_anlys_event_study_model_log_fixed_lin_time)
##
## Call:
## lm(formula = formula_event_study_log_fixed_lin_time, data = sensitivity_anlys_event_study_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.94531 -0.13453 0.01384 0.15668 1.02461
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.075e+01 9.544e-02 -112.655 < 2e-16 ***
## StateAlaska 3.681e-01 1.075e-01 3.426 0.000626 ***
## StateArizona 5.417e-01 9.088e-02 5.961 2.99e-09 ***
## StateArkansas -5.239e-01 7.259e-02 -7.216 7.74e-13 ***
## StateCalifornia 2.073e-01 1.047e-01 1.979 0.047963 *
## StateColorado 2.631e-01 9.303e-02 2.828 0.004731 **
## StateConnecticut 9.640e-02 9.110e-02 1.058 0.290105
## StateDelaware 1.371e-01 9.579e-02 1.431 0.152515
## StateFlorida 4.217e-01 8.768e-02 4.810 1.63e-06 ***
## StateGeorgia 1.256e-01 9.359e-02 1.342 0.179679
## StateHawaii -1.940e-01 9.856e-02 -1.968 0.049189 *
## StateIdaho 1.268e-01 1.020e-01 1.244 0.213751
## StateIllinois 6.142e-02 9.772e-02 0.629 0.529744
## StateIndiana -7.033e-02 8.764e-02 -0.802 0.422390
## StateIowa -7.574e-01 9.173e-02 -8.257 2.80e-16 ***
## StateKansas -3.589e-01 8.637e-02 -4.155 3.40e-05 ***
## StateKentucky 6.751e-01 7.308e-02 9.238 < 2e-16 ***
## StateLouisiana 4.021e-01 7.420e-02 5.419 6.78e-08 ***
## StateMaine -6.443e-02 9.467e-02 -0.681 0.496190
## StateMaryland -1.450e+00 8.167e-02 -17.755 < 2e-16 ***
## StateMassachusetts -2.100e-01 9.102e-02 -2.307 0.021172 *
## StateMichigan -8.755e-02 8.965e-02 -0.977 0.328865
## StateMinnesota -8.065e-01 8.839e-02 -9.124 < 2e-16 ***
## StateMississippi -9.381e-02 8.422e-02 -1.114 0.265434
## StateMissouri 4.407e-02 9.107e-02 0.484 0.628464
## StateMontana -1.026e-01 9.498e-02 -1.080 0.280276
## StateNebraska -1.044e+00 9.408e-02 -11.101 < 2e-16 ***
## StateNevada 7.785e-01 9.129e-02 8.527 < 2e-16 ***
## StateNew Hampshire -2.938e-03 9.185e-02 -0.032 0.974486
## StateNew Jersey 1.872e-02 1.003e-01 0.187 0.851990
## StateNew Mexico 8.850e-01 8.919e-02 9.923 < 2e-16 ***
## StateNew York -2.568e-01 9.076e-02 -2.830 0.004707 **
## StateNorth Carolina 2.672e-01 7.077e-02 3.776 0.000164 ***
## StateNorth Dakota -1.325e+00 9.366e-02 -14.146 < 2e-16 ***
## StateOhio 4.498e-01 1.090e-01 4.128 3.83e-05 ***
## StateOklahoma 4.440e-01 7.182e-02 6.181 7.79e-10 ***
## StateOregon -4.697e-02 8.988e-02 -0.523 0.601342
## StatePennsylvania 5.675e-01 1.067e-01 5.316 1.19e-07 ***
## StateRhode Island -4.515e-01 1.034e-01 -4.368 1.32e-05 ***
## StateSouth Carolina 1.590e-01 9.194e-02 1.730 0.083853 .
## StateSouth Dakota -1.233e+00 1.078e-01 -11.438 < 2e-16 ***
## StateTennessee 4.662e-01 6.651e-02 7.009 3.34e-12 ***
## StateTexas 9.686e-02 8.446e-02 1.147 0.251623
## StateUtah 2.479e-01 8.977e-02 2.761 0.005817 **
## StateVermont -3.360e-01 9.209e-02 -3.648 0.000271 ***
## StateVirginia 3.640e-02 7.555e-02 0.482 0.629990
## StateWashington 2.882e-01 8.980e-02 3.210 0.001351 **
## StateWest Virginia 7.654e-01 7.839e-02 9.763 < 2e-16 ***
## StateWisconsin -8.544e-02 9.307e-02 -0.918 0.358705
## StateWyoming 2.723e-01 8.661e-02 3.144 0.001695 **
## Naloxone_Pharmacy_Yes_Redefined 5.742e-02 3.942e-02 1.457 0.145393
## Naloxone_Pharmacy_No_Redefined 1.750e-02 3.877e-02 0.452 0.651676
## Medical_Marijuana_Redefined 2.179e-01 3.148e-02 6.922 6.11e-12 ***
## Recreational_Marijuana_Redefined -7.658e-02 4.945e-02 -1.549 0.121609
## GSL_Redefined 5.952e-02 3.170e-02 1.877 0.060623 .
## PDMP_Redefined -1.878e-01 2.513e-02 -7.472 1.20e-13 ***
## Medicaid_Expansion_Redefined 7.906e-02 3.021e-02 2.617 0.008940 **
## neg_2_pd 2.811e-02 6.097e-02 0.461 0.644868
## neg_3_pd 3.165e-02 6.190e-02 0.511 0.609135
## neg_4_pd 7.850e-03 6.316e-02 0.124 0.901104
## neg_5_pd 3.932e-03 6.385e-02 0.062 0.950903
## neg_6_pd 7.330e-03 6.594e-02 0.111 0.911513
## neg_7_pd -4.042e-02 6.705e-02 -0.603 0.546673
## neg_8_pd -1.028e-01 6.875e-02 -1.496 0.134855
## neg_9_pd -3.113e-02 7.163e-02 -0.435 0.663913
## neg_10_pd 1.448e-02 7.375e-02 0.196 0.844339
## neg_11_pd 1.979e-02 7.618e-02 0.260 0.795086
## neg_12_pd 1.120e-01 8.058e-02 1.390 0.164807
## neg_13_pd 1.633e-02 8.271e-02 0.197 0.843482
## neg_14_pd -1.026e-02 8.494e-02 -0.121 0.903825
## neg_15_pd -5.217e-02 8.733e-02 -0.597 0.550303
## neg_16_pd -3.652e-02 9.162e-02 -0.399 0.690262
## neg_17_pd -4.312e-02 9.690e-02 -0.445 0.656356
## neg_18_pd -3.964e-02 1.003e-01 -0.395 0.692646
## neg_19_pd -1.457e-01 1.036e-01 -1.407 0.159592
## neg_20_pd -1.913e-01 1.096e-01 -1.745 0.081105 .
## neg_21_pd -1.223e-01 1.168e-01 -1.048 0.294990
## neg_22_pd -1.057e-01 1.195e-01 -0.885 0.376474
## neg_23_pd -1.248e-01 1.238e-01 -1.008 0.313537
## neg_24_pd -1.803e-01 1.330e-01 -1.355 0.175496
## neg_25_pd -4.070e-02 1.356e-01 -0.300 0.764130
## neg_26_pd 3.718e-02 1.414e-01 0.263 0.792632
## neg_27_pd -2.152e-01 1.570e-01 -1.371 0.170645
## neg_28_pd -2.102e-01 1.595e-01 -1.318 0.187786
## neg_29_pd 5.712e-03 1.686e-01 0.034 0.972974
## neg_30_pd -6.349e-02 1.793e-01 -0.354 0.723254
## neg_31_pd -7.353e-02 1.818e-01 -0.404 0.685918
## neg_32_pd -5.692e-03 1.968e-01 -0.029 0.976933
## neg_33_pd 6.658e-02 2.498e-01 0.267 0.789851
## pos_0_pd -2.301e-02 6.072e-02 -0.379 0.704770
## pos_1_pd -5.961e-02 6.127e-02 -0.973 0.330724
## pos_2_pd -2.841e-02 6.204e-02 -0.458 0.647008
## pos_3_pd -6.438e-02 6.304e-02 -1.021 0.307267
## pos_4_pd -6.953e-02 6.423e-02 -1.082 0.279202
## pos_5_pd -1.105e-01 6.567e-02 -1.682 0.092724 .
## pos_6_pd -1.105e-01 6.749e-02 -1.637 0.101807
## pos_7_pd -1.066e-01 6.950e-02 -1.534 0.125178
## pos_8_pd -1.617e-01 7.211e-02 -2.243 0.025007 *
## pos_9_pd -1.812e-01 7.458e-02 -2.429 0.015225 *
## pos_10_pd -1.955e-01 7.677e-02 -2.546 0.010965 *
## pos_11_pd -1.992e-01 7.945e-02 -2.508 0.012236 *
## pos_12_pd -2.016e-01 8.223e-02 -2.451 0.014333 *
## pos_13_pd -2.705e-01 8.478e-02 -3.191 0.001444 **
## pos_14_pd -2.628e-01 8.835e-02 -2.975 0.002969 **
## pos_15_pd -2.708e-01 9.162e-02 -2.956 0.003159 **
## pos_16_pd -2.885e-01 9.454e-02 -3.051 0.002311 **
## pos_17_pd -2.850e-01 9.847e-02 -2.894 0.003851 **
## pos_18_pd -2.747e-01 1.020e-01 -2.694 0.007123 **
## pos_19_pd -2.633e-01 1.049e-01 -2.511 0.012133 *
## pos_20_pd -2.747e-01 1.092e-01 -2.517 0.011935 *
## pos_21_pd -3.075e-01 1.135e-01 -2.708 0.006830 **
## pos_22_pd -3.064e-01 1.171e-01 -2.617 0.008954 **
## pos_23_pd -3.240e-01 1.211e-01 -2.675 0.007548 **
## pos_24_pd -3.686e-01 1.266e-01 -2.911 0.003643 **
## pos_25_pd -3.300e-01 1.319e-01 -2.502 0.012447 *
## pos_26_pd -3.265e-01 1.352e-01 -2.415 0.015810 *
## pos_27_pd -3.660e-01 1.389e-01 -2.636 0.008465 **
## pos_28_pd -3.402e-01 1.420e-01 -2.395 0.016699 *
## pos_29_pd -3.473e-01 1.495e-01 -2.323 0.020313 *
## pos_30_pd -2.843e-01 1.542e-01 -1.844 0.065313 .
## pos_31_pd -2.447e-01 1.595e-01 -1.534 0.125160
## pos_32_pd -3.009e-01 1.696e-01 -1.774 0.076169 .
## pos_33_pd -3.286e-01 1.760e-01 -1.867 0.062044 .
## pos_34_pd -3.185e-01 1.793e-01 -1.777 0.075803 .
## pos_35_pd -5.112e-01 1.958e-01 -2.611 0.009092 **
## pos_36_pd -5.411e-01 1.988e-01 -2.721 0.006568 **
## pos_37_pd -5.613e-01 2.208e-01 -2.542 0.011107 *
## pos_38_pd -5.073e-01 2.698e-01 -1.880 0.060223 .
## pos_39_pd -5.236e-01 2.725e-01 -1.921 0.054831 .
## Time_Period_ID:RegionMidwest 8.336e-02 6.350e-03 13.128 < 2e-16 ***
## Time_Period_ID:RegionNortheast 6.990e-02 7.238e-03 9.657 < 2e-16 ***
## Time_Period_ID:RegionSouth 7.534e-02 6.113e-03 12.326 < 2e-16 ***
## Time_Period_ID:RegionWest 5.984e-02 6.325e-03 9.460 < 2e-16 ***
## RegionMidwest:I(Time_Period_ID^2) -7.722e-04 1.317e-04 -5.865 5.29e-09 ***
## RegionNortheast:I(Time_Period_ID^2) -3.276e-04 1.529e-04 -2.142 0.032326 *
## RegionSouth:I(Time_Period_ID^2) -7.387e-04 1.228e-04 -6.017 2.13e-09 ***
## RegionWest:I(Time_Period_ID^2) -6.900e-04 1.325e-04 -5.206 2.15e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.297 on 1863 degrees of freedom
## Multiple R-squared: 0.8471, Adjusted R-squared: 0.8359
## F-statistic: 75.9 on 136 and 1863 DF, p-value: < 2.2e-16
Sandwich Estimator
#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_event_study_log_fixed_lin_time <-
model.matrix(sensitivity_anlys_event_study_model_log_fixed_lin_time)
#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_event_study_log_fixed_lin_time <- coef(sensitivity_anlys_event_study_model_log_fixed_lin_time)
#type = "response" to get the estimated probabilities
sensitivity_anlys_event_study_sd_and_ci_log_fixed_lin_time <-
compute_sd_and_CI((full_df_w_basis_functions_sensitivity_anlys_event_study_log_fixed_lin_time),
log(sensitivity_anlys_event_study_data$prop_dead),
coefficient_values_sensitivity_anlys_event_study_log_fixed_lin_time,
p = ncol(full_df_w_basis_functions_sensitivity_anlys_event_study_log_fixed_lin_time) - 50)
(sensitivity_anlys_event_study_sd_and_ci_log_fixed_lin_time)
## lb_coef coef_values ub_coef
## (Intercept) -1.089285e+01 -1.075211e+01 -1.061138e+01
## StateAlaska 2.050016e-01 3.681466e-01 5.312917e-01
## StateArizona 3.960676e-01 5.417212e-01 6.873748e-01
## StateArkansas -6.289267e-01 -5.238541e-01 -4.187814e-01
## StateCalifornia 2.472627e-02 2.072651e-01 3.898039e-01
## StateColorado 1.189345e-01 2.631204e-01 4.073063e-01
## StateConnecticut -1.382673e-01 9.640148e-02 3.310702e-01
## StateDelaware -1.978970e-06 1.370999e-01 2.742017e-01
## StateFlorida 3.022941e-01 4.217490e-01 5.412040e-01
## StateGeorgia 9.803159e-03 1.256264e-01 2.414496e-01
## StateHawaii -3.545868e-01 -1.939821e-01 -3.337747e-02
## StateIdaho -2.296005e-02 1.268318e-01 2.766236e-01
## StateIllinois -1.145279e-01 6.141792e-02 2.373637e-01
## StateIndiana -2.158224e-01 -7.032763e-02 7.516715e-02
## StateIowa -9.071543e-01 -7.573683e-01 -6.075824e-01
## StateKansas -4.940425e-01 -3.589045e-01 -2.237665e-01
## StateKentucky 5.803174e-01 6.751092e-01 7.699011e-01
## StateLouisiana 2.966035e-01 4.020635e-01 5.075235e-01
## StateMaine -3.073809e-01 -6.443333e-02 1.785142e-01
## StateMaryland -1.663525e+00 -1.450107e+00 -1.236689e+00
## StateMassachusetts -5.496039e-01 -2.099646e-01 1.296747e-01
## StateMichigan -2.243753e-01 -8.755277e-02 4.926972e-02
## StateMinnesota -9.512138e-01 -8.064512e-01 -6.616885e-01
## StateMississippi -2.173607e-01 -9.381424e-02 2.973222e-02
## StateMissouri -9.498085e-02 4.407434e-02 1.831295e-01
## StateMontana -2.617755e-01 -1.025779e-01 5.661976e-02
## StateNebraska -1.183936e+00 -1.044406e+00 -9.048764e-01
## StateNevada 6.290268e-01 7.784794e-01 9.279319e-01
## StateNew Hampshire -2.286859e-01 -2.937945e-03 2.228100e-01
## StateNew Jersey -2.265469e-01 1.872191e-02 2.639907e-01
## StateNew Mexico 7.189691e-01 8.850272e-01 1.051085e+00
## StateNew York -4.818839e-01 -2.568378e-01 -3.179176e-02
## StateNorth Carolina 1.747784e-01 2.672113e-01 3.596442e-01
## StateNorth Dakota -1.510377e+00 -1.324860e+00 -1.139343e+00
## StateOhio 2.792821e-01 4.498463e-01 6.204106e-01
## StateOklahoma 3.296251e-01 4.439738e-01 5.583225e-01
## StateOregon -1.912956e-01 -4.696872e-02 9.735814e-02
## StatePennsylvania 3.497080e-01 5.674613e-01 7.852145e-01
## StateRhode Island -8.254178e-01 -4.515446e-01 -7.767130e-02
## StateSouth Carolina 4.291673e-02 1.590223e-01 2.751279e-01
## StateSouth Dakota -1.392377e+00 -1.233372e+00 -1.074367e+00
## StateTennessee 3.771601e-01 4.661888e-01 5.552175e-01
## StateTexas -2.407234e-02 9.685755e-02 2.177874e-01
## StateUtah 1.612987e-02 2.478713e-01 4.796127e-01
## StateVermont -5.828738e-01 -3.359903e-01 -8.910678e-02
## StateVirginia -6.377525e-02 3.640333e-02 1.365819e-01
## StateWashington 1.422529e-01 2.882373e-01 4.342217e-01
## StateWest Virginia 6.203789e-01 7.653531e-01 9.103272e-01
## StateWisconsin -2.231358e-01 -8.544359e-02 5.224862e-02
## StateWyoming 1.008182e-01 2.722705e-01 4.437228e-01
## Naloxone_Pharmacy_Yes_Redefined -5.203160e-03 5.742059e-02 1.200443e-01
## Naloxone_Pharmacy_No_Redefined -4.396766e-02 1.750351e-02 7.897469e-02
## Medical_Marijuana_Redefined 1.483510e-01 2.179011e-01 2.874511e-01
## Recreational_Marijuana_Redefined -1.550340e-01 -7.658036e-02 1.873229e-03
## GSL_Redefined 6.228085e-03 5.951552e-02 1.128030e-01
## PDMP_Redefined -2.419083e-01 -1.878129e-01 -1.337176e-01
## Medicaid_Expansion_Redefined 2.919047e-02 7.905536e-02 1.289203e-01
## neg_2_pd -8.656997e-02 2.810796e-02 1.427859e-01
## neg_3_pd -8.212587e-02 3.165424e-02 1.454344e-01
## neg_4_pd -1.116155e-01 7.849767e-03 1.273150e-01
## neg_5_pd -1.122759e-01 3.931807e-03 1.201396e-01
## neg_6_pd -1.019467e-01 7.329461e-03 1.166056e-01
## neg_7_pd -1.541889e-01 -4.041923e-02 7.335044e-02
## neg_8_pd -2.464440e-01 -1.028469e-01 4.075008e-02
## neg_9_pd -1.839498e-01 -3.112932e-02 1.216912e-01
## neg_10_pd -1.256026e-01 1.448313e-02 1.545689e-01
## neg_11_pd -1.266113e-01 1.978697e-02 1.661852e-01
## neg_12_pd -4.910051e-02 1.119802e-01 2.730609e-01
## neg_13_pd -1.498086e-01 1.633347e-02 1.824756e-01
## neg_14_pd -1.667126e-01 -1.026441e-02 1.461838e-01
## neg_15_pd -2.440489e-01 -5.217270e-02 1.397035e-01
## neg_16_pd -2.159398e-01 -3.651798e-02 1.429038e-01
## neg_17_pd -1.932700e-01 -4.312360e-02 1.070228e-01
## neg_18_pd -1.807824e-01 -3.964077e-02 1.015009e-01
## neg_19_pd -3.791164e-01 -1.457109e-01 8.769464e-02
## neg_20_pd -4.528917e-01 -1.913222e-01 7.024731e-02
## neg_21_pd -3.065006e-01 -1.223277e-01 6.184521e-02
## neg_22_pd -2.967386e-01 -1.057079e-01 8.532286e-02
## neg_23_pd -4.106297e-01 -1.248126e-01 1.610045e-01
## neg_24_pd -5.206480e-01 -1.803116e-01 1.600248e-01
## neg_25_pd -3.255205e-01 -4.069763e-02 2.441253e-01
## neg_26_pd -3.168582e-01 3.718388e-02 3.912259e-01
## neg_27_pd -7.086401e-01 -2.151989e-01 2.782424e-01
## neg_28_pd -6.790181e-01 -2.102090e-01 2.586002e-01
## neg_29_pd -2.710709e-01 5.712051e-03 2.824950e-01
## neg_30_pd -3.072519e-01 -6.348969e-02 1.802726e-01
## neg_31_pd -2.716534e-01 -7.352839e-02 1.245966e-01
## neg_32_pd -1.928487e-01 -5.691465e-03 1.814658e-01
## neg_33_pd -2.064491e-01 6.658465e-02 3.396184e-01
## pos_0_pd -1.302889e-01 -2.301035e-02 8.426815e-02
## pos_1_pd -1.751046e-01 -5.961202e-02 5.588056e-02
## pos_2_pd -1.332546e-01 -2.841288e-02 7.642883e-02
## pos_3_pd -1.712859e-01 -6.437589e-02 4.253413e-02
## pos_4_pd -1.774399e-01 -6.952593e-02 3.838809e-02
## pos_5_pd -2.200513e-01 -1.104613e-01 -8.713108e-04
## pos_6_pd -2.245296e-01 -1.104797e-01 3.570095e-03
## pos_7_pd -2.250933e-01 -1.066177e-01 1.185801e-02
## pos_8_pd -2.753291e-01 -1.617419e-01 -4.815471e-02
## pos_9_pd -3.017241e-01 -1.811803e-01 -6.063641e-02
## pos_10_pd -3.186313e-01 -1.954766e-01 -7.232188e-02
## pos_11_pd -3.153751e-01 -1.992250e-01 -8.307492e-02
## pos_12_pd -3.233313e-01 -2.015583e-01 -7.978523e-02
## pos_13_pd -4.078027e-01 -2.704839e-01 -1.331650e-01
## pos_14_pd -4.029773e-01 -2.628264e-01 -1.226756e-01
## pos_15_pd -4.045901e-01 -2.707898e-01 -1.369896e-01
## pos_16_pd -4.280635e-01 -2.884658e-01 -1.488681e-01
## pos_17_pd -4.275803e-01 -2.849580e-01 -1.423356e-01
## pos_18_pd -4.185349e-01 -2.746873e-01 -1.308398e-01
## pos_19_pd -4.031417e-01 -2.632743e-01 -1.234069e-01
## pos_20_pd -4.231130e-01 -2.747120e-01 -1.263110e-01
## pos_21_pd -4.659699e-01 -3.074532e-01 -1.489365e-01
## pos_22_pd -4.630366e-01 -3.064491e-01 -1.498616e-01
## pos_23_pd -4.914538e-01 -3.239828e-01 -1.565117e-01
## pos_24_pd -5.457113e-01 -3.686145e-01 -1.915176e-01
## pos_25_pd -5.270883e-01 -3.300315e-01 -1.329747e-01
## pos_26_pd -5.178228e-01 -3.264909e-01 -1.351591e-01
## pos_27_pd -5.662755e-01 -3.659712e-01 -1.656668e-01
## pos_28_pd -5.474045e-01 -3.401865e-01 -1.329686e-01
## pos_29_pd -5.676360e-01 -3.472889e-01 -1.269419e-01
## pos_30_pd -5.115678e-01 -2.842876e-01 -5.700734e-02
## pos_31_pd -4.972488e-01 -2.446719e-01 7.904913e-03
## pos_32_pd -5.469828e-01 -3.009225e-01 -5.486222e-02
## pos_33_pd -6.272617e-01 -3.285532e-01 -2.984473e-02
## pos_34_pd -6.233627e-01 -3.184672e-01 -1.357177e-02
## pos_35_pd -7.761763e-01 -5.111925e-01 -2.462088e-01
## pos_36_pd -8.095707e-01 -5.410749e-01 -2.725791e-01
## pos_37_pd -8.184267e-01 -5.612764e-01 -3.041260e-01
## pos_38_pd -7.329770e-01 -5.073394e-01 -2.817017e-01
## pos_39_pd -8.075909e-01 -5.235895e-01 -2.395881e-01
## Time_Period_ID:RegionMidwest 7.397223e-02 8.336186e-02 9.275149e-02
## Time_Period_ID:RegionNortheast 4.962925e-02 6.989915e-02 9.016906e-02
## Time_Period_ID:RegionSouth 6.648278e-02 7.534090e-02 8.419902e-02
## Time_Period_ID:RegionWest 4.990702e-02 5.983841e-02 6.976980e-02
## RegionMidwest:I(Time_Period_ID^2) -9.929257e-04 -7.722261e-04 -5.515265e-04
## RegionNortheast:I(Time_Period_ID^2) -7.565513e-04 -3.275860e-04 1.013793e-04
## RegionSouth:I(Time_Period_ID^2) -9.541258e-04 -7.387434e-04 -5.233611e-04
## RegionWest:I(Time_Period_ID^2) -9.292071e-04 -6.900113e-04 -4.508155e-04
## sd_coef
## (Intercept) 0.0718047299
## StateAlaska 0.0832372748
## StateArizona 0.0743130609
## StateArkansas 0.0536084973
## StateCalifornia 0.0931320602
## StateColorado 0.0735642383
## StateConnecticut 0.1197289584
## StateDelaware 0.0699499164
## StateFlorida 0.0609464175
## StateGeorgia 0.0590934744
## StateHawaii 0.0819411586
## StateIdaho 0.0764244081
## StateIllinois 0.0897682752
## StateIndiana 0.0742320278
## StateIowa 0.0764214032
## StateKansas 0.0689479782
## StateKentucky 0.0483631662
## StateLouisiana 0.0538061113
## StateMaine 0.1239528437
## StateMaryland 0.1088867710
## StateMassachusetts 0.1732853548
## StateMichigan 0.0698073951
## StateMinnesota 0.0738584885
## StateMississippi 0.0630339094
## StateMissouri 0.0709465264
## StateMontana 0.0812232925
## StateNebraska 0.0711886816
## StateNevada 0.0762513103
## StateNew Hampshire 0.1151775481
## StateNew Jersey 0.1251371438
## StateNew Mexico 0.0847235288
## StateNew York 0.1148194152
## StateNorth Carolina 0.0471596345
## StateNorth Dakota 0.0946514407
## StateOhio 0.0870225705
## StateOklahoma 0.0583411725
## StateOregon 0.0736361494
## StatePennsylvania 0.1110986000
## StateRhode Island 0.1907516664
## StateSouth Carolina 0.0592375482
## StateSouth Dakota 0.0811248893
## StateTennessee 0.0454227853
## StateTexas 0.0616989197
## StateUtah 0.1182354224
## StateVermont 0.1259609766
## StateVirginia 0.0511115207
## StateWashington 0.0744818207
## StateWest Virginia 0.0739664162
## StateWisconsin 0.0702511274
## StateWyoming 0.0874756561
## Naloxone_Pharmacy_Yes_Redefined 0.0319508935
## Naloxone_Pharmacy_No_Redefined 0.0313628443
## Medical_Marijuana_Redefined 0.0354847320
## Recreational_Marijuana_Redefined 0.0400273424
## GSL_Redefined 0.0271874677
## PDMP_Redefined 0.0275996576
## Medicaid_Expansion_Redefined 0.0254412709
## neg_2_pd 0.0585091490
## neg_3_pd 0.0580510764
## neg_4_pd 0.0609516608
## neg_5_pd 0.0592896684
## neg_6_pd 0.0557531504
## neg_7_pd 0.0580457526
## neg_8_pd 0.0732637884
## neg_9_pd 0.0779696455
## neg_10_pd 0.0714723204
## neg_11_pd 0.0746929898
## neg_12_pd 0.0821840333
## neg_13_pd 0.0847663808
## neg_14_pd 0.0798205026
## neg_15_pd 0.0978960169
## neg_16_pd 0.0915417272
## neg_17_pd 0.0766053262
## neg_18_pd 0.0720110493
## neg_19_pd 0.1190844558
## neg_20_pd 0.1334538192
## neg_21_pd 0.0939657677
## neg_22_pd 0.0974646494
## neg_23_pd 0.1458250391
## neg_24_pd 0.1736410354
## neg_25_pd 0.1453178004
## neg_26_pd 0.1806336937
## neg_27_pd 0.2517557402
## neg_28_pd 0.2391883334
## neg_29_pd 0.1412158156
## neg_30_pd 0.1243684913
## neg_31_pd 0.1010841727
## neg_32_pd 0.0954883973
## neg_33_pd 0.1393029095
## pos_0_pd 0.0547339304
## pos_1_pd 0.0589247869
## pos_2_pd 0.0534906706
## pos_3_pd 0.0545459288
## pos_4_pd 0.0550581698
## pos_5_pd 0.0559132579
## pos_6_pd 0.0581886948
## pos_7_pd 0.0604467726
## pos_8_pd 0.0579526492
## pos_9_pd 0.0615019738
## pos_10_pd 0.0628340417
## pos_11_pd 0.0592602451
## pos_12_pd 0.0621290999
## pos_13_pd 0.0700606364
## pos_14_pd 0.0715055328
## pos_15_pd 0.0682654242
## pos_16_pd 0.0712233271
## pos_17_pd 0.0727665048
## pos_18_pd 0.0733916212
## pos_19_pd 0.0713609319
## pos_20_pd 0.0757148028
## pos_21_pd 0.0808758736
## pos_22_pd 0.0798915755
## pos_23_pd 0.0854444121
## pos_24_pd 0.0903555345
## pos_25_pd 0.1005391782
## pos_26_pd 0.0976182739
## pos_27_pd 0.1021960940
## pos_28_pd 0.1057234454
## pos_29_pd 0.1124219691
## pos_30_pd 0.1159592983
## pos_31_pd 0.1288657409
## pos_32_pd 0.1255409744
## pos_33_pd 0.1524022820
## pos_34_pd 0.1555589153
## pos_35_pd 0.1351957862
## pos_36_pd 0.1369876529
## pos_37_pd 0.1311991615
## pos_38_pd 0.1151212479
## pos_39_pd 0.1448986784
## Time_Period_ID:RegionMidwest 0.0047906273
## Time_Period_ID:RegionNortheast 0.0103417863
## Time_Period_ID:RegionSouth 0.0045194473
## Time_Period_ID:RegionWest 0.0050670362
## RegionMidwest:I(Time_Period_ID^2) 0.0001126018
## RegionNortheast:I(Time_Period_ID^2) 0.0002188598
## RegionSouth:I(Time_Period_ID^2) 0.0001098890
## RegionWest:I(Time_Period_ID^2) 0.0001220387
# write.csv(round(sensitivity_anlys_event_study_sd_and_ci, 3), "./Data/event_study_coef_and_ci.csv")
Plot Results
#plot the coefficients for the periods before and after the intervention with 95% CI
plot_event_study_log_fixed_lin_time <- sensitivity_anlys_event_study_sd_and_ci_log_fixed_lin_time %>%
mutate(term = rownames(sensitivity_anlys_event_study_sd_and_ci_log_fixed_lin_time)) %>%
dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
filter(term %in% c(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2),
function(x){paste("neg_", x, "_pd", sep = "")}),
sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_event_study_log_fixed_lin_time) <- c("term", "estimate", "conf.low", "conf.high")
dwplot(plot_event_study_log_fixed_lin_time, colour = "black",
vars_order = c(sapply((max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0,
function(x){paste("pos_", x, "_pd", sep = "")}),
sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2),
function(x){paste("neg_", x, "_pd", sep = "")}))) +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black"),
axis.text.x = element_text(angle = 45)) +
geom_vline(aes(xintercept = 0), linetype = "dashed") +
labs(y = "States Excluded", x = "Coefficients and 95% Confidence Intervals",
title = "Coefficient of Pre-Intervention and Post-Intervention Periods") +
scale_color_grey() +
coord_flip() +
geom_hline(yintercept = 33, col = "red", linetype = "dashed")
Event Study with Model SD
SD Estimator
summary_model_log_fixed_lin_time <- summary(sensitivity_anlys_event_study_model_log_fixed_lin_time)
coef_log_fixed_lin_time <- data.frame(coef_values = summary_model_log_fixed_lin_time$coefficients[,1],
lb_coef = summary_model_log_fixed_lin_time$coefficients[,1] -
1.96*summary_model_log_fixed_lin_time$coefficients[,2],
ub_coef = summary_model_log_fixed_lin_time$coefficients[,1] +
1.96*summary_model_log_fixed_lin_time$coefficients[,2])
Plot Results
#plot the coefficients for the periods before and after the intervention with 95% CI
plot_event_study_log_fixed_lin_time_model_sd <- coef_log_fixed_lin_time %>%
mutate(term = rownames(coef_log_fixed_lin_time)) %>%
dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
filter(term %in% c(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2),
function(x){paste("neg_", x, "_pd", sep = "")}),
sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_event_study_log_fixed_lin_time_model_sd) <- c("term", "estimate", "conf.low", "conf.high")
dwplot(plot_event_study_log_fixed_lin_time_model_sd, colour = "black",
vars_order = c(sapply((max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0,
function(x){paste("pos_", x, "_pd", sep = "")}),
sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2),
function(x){paste("neg_", x, "_pd", sep = "")}))) +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black"),
axis.text.x = element_text(angle = 45)) +
geom_vline(aes(xintercept = 0), linetype = "dashed") +
labs(y = "States Excluded", x = "Coefficients and 95% Confidence Intervals",
title = "Coefficient of Pre-Intervention and Post-Intervention Periods") +
scale_color_grey() +
coord_flip() +
geom_hline(yintercept = 33, col = "red", linetype = "dashed")
Analysis With Only Periods After Treatment
formula_post_tx_log_fixed_lin_time <- formula(paste("log(prop_dead)~ State +
Time_Period_ID:Region +
I(Time_Period_ID^2):Region +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +",
paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_post_tx_model_log_fixed_lin_time<-lm(formula_post_tx_log_fixed_lin_time,
data = sensitivity_anlys_event_study_data)
summary(sensitivity_anlys_post_tx_model_log_fixed_lin_time)
##
## Call:
## lm(formula = formula_post_tx_log_fixed_lin_time, data = sensitivity_anlys_event_study_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.02721 -0.13368 0.01535 0.15896 1.01698
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.080e+01 5.921e-02 -182.420 < 2e-16 ***
## StateAlaska 2.967e-01 8.967e-02 3.309 0.000954 ***
## StateArizona 4.987e-01 8.586e-02 5.808 7.40e-09 ***
## StateArkansas -5.591e-01 6.798e-02 -8.225 3.59e-16 ***
## StateCalifornia 2.543e-01 9.219e-02 2.759 0.005853 **
## StateColorado 2.249e-01 8.912e-02 2.524 0.011690 *
## StateConnecticut 1.058e-01 9.005e-02 1.175 0.240113
## StateDelaware 6.701e-02 7.023e-02 0.954 0.340179
## StateFlorida 4.733e-01 7.108e-02 6.658 3.62e-11 ***
## StateGeorgia 1.862e-01 7.271e-02 2.561 0.010528 *
## StateHawaii -2.335e-01 8.970e-02 -2.604 0.009294 **
## StateIdaho 5.990e-02 8.696e-02 0.689 0.491038
## StateIllinois 1.075e-01 8.783e-02 1.225 0.220913
## StateIndiana -8.394e-02 8.651e-02 -0.970 0.331978
## StateIowa -7.274e-01 8.635e-02 -8.424 < 2e-16 ***
## StateKansas -3.463e-01 8.567e-02 -4.042 5.50e-05 ***
## StateKentucky 6.379e-01 6.792e-02 9.392 < 2e-16 ***
## StateLouisiana 4.279e-01 6.774e-02 6.317 3.32e-10 ***
## StateMaine -6.923e-02 9.276e-02 -0.746 0.455563
## StateMaryland -1.409e+00 7.030e-02 -20.042 < 2e-16 ***
## StateMassachusetts -2.044e-01 8.995e-02 -2.273 0.023163 *
## StateMichigan -6.756e-02 8.707e-02 -0.776 0.437842
## StateMinnesota -7.958e-01 8.774e-02 -9.070 < 2e-16 ***
## StateMississippi -1.571e-01 6.783e-02 -2.316 0.020656 *
## StateMissouri 6.991e-02 8.739e-02 0.800 0.423777
## StateMontana -7.476e-02 8.823e-02 -0.847 0.396923
## StateNebraska -1.082e+00 8.754e-02 -12.362 < 2e-16 ***
## StateNevada 7.920e-01 8.866e-02 8.933 < 2e-16 ***
## StateNew Hampshire -1.481e-02 8.975e-02 -0.165 0.868915
## StateNew Jersey 6.674e-02 9.089e-02 0.734 0.462820
## StateNew Mexico 8.669e-01 8.813e-02 9.836 < 2e-16 ***
## StateNew York -2.457e-01 8.967e-02 -2.740 0.006203 **
## StateNorth Carolina 2.847e-01 6.712e-02 4.242 2.32e-05 ***
## StateNorth Dakota -1.364e+00 8.688e-02 -15.699 < 2e-16 ***
## StateOhio 5.175e-01 8.962e-02 5.774 9.00e-09 ***
## StateOklahoma 4.109e-01 6.754e-02 6.083 1.42e-09 ***
## StateOregon -6.071e-02 8.896e-02 -0.682 0.495062
## StatePennsylvania 6.255e-01 9.318e-02 6.713 2.52e-11 ***
## StateRhode Island -5.083e-01 9.098e-02 -5.587 2.64e-08 ***
## StateSouth Carolina 8.840e-02 6.844e-02 1.292 0.196611
## StateSouth Dakota -1.296e+00 8.821e-02 -14.690 < 2e-16 ***
## StateTennessee 4.656e-01 6.645e-02 7.007 3.38e-12 ***
## StateTexas 1.433e-01 7.069e-02 2.027 0.042752 *
## StateUtah 2.650e-01 8.636e-02 3.069 0.002177 **
## StateVermont -3.443e-01 9.008e-02 -3.822 0.000136 ***
## StateVirginia 6.727e-02 6.809e-02 0.988 0.323272
## StateWashington 2.842e-01 8.938e-02 3.179 0.001500 **
## StateWest Virginia 7.171e-01 6.823e-02 10.510 < 2e-16 ***
## StateWisconsin -5.121e-02 8.648e-02 -0.592 0.553788
## StateWyoming 2.618e-01 8.589e-02 3.048 0.002333 **
## Naloxone_Pharmacy_Yes_Redefined 5.810e-02 3.932e-02 1.478 0.139643
## Naloxone_Pharmacy_No_Redefined 1.576e-02 3.864e-02 0.408 0.683337
## Medical_Marijuana_Redefined 2.221e-01 3.123e-02 7.114 1.59e-12 ***
## Recreational_Marijuana_Redefined -7.031e-02 4.881e-02 -1.440 0.149917
## GSL_Redefined 5.969e-02 3.161e-02 1.888 0.059123 .
## PDMP_Redefined -1.832e-01 2.473e-02 -7.407 1.94e-13 ***
## Medicaid_Expansion_Redefined 7.554e-02 3.002e-02 2.517 0.011931 *
## pos_0_pd -4.391e-02 4.635e-02 -0.948 0.343494
## pos_1_pd -8.452e-02 4.681e-02 -1.805 0.071162 .
## pos_2_pd -5.723e-02 4.729e-02 -1.210 0.226343
## pos_3_pd -9.708e-02 4.785e-02 -2.029 0.042608 *
## pos_4_pd -1.061e-01 4.845e-02 -2.189 0.028738 *
## pos_5_pd -1.506e-01 4.925e-02 -3.057 0.002265 **
## pos_6_pd -1.542e-01 5.022e-02 -3.071 0.002165 **
## pos_7_pd -1.543e-01 5.111e-02 -3.019 0.002566 **
## pos_8_pd -2.137e-01 5.253e-02 -4.068 4.94e-05 ***
## pos_9_pd -2.373e-01 5.371e-02 -4.417 1.06e-05 ***
## pos_10_pd -2.554e-01 5.451e-02 -4.685 3.00e-06 ***
## pos_11_pd -2.633e-01 5.570e-02 -4.727 2.45e-06 ***
## pos_12_pd -2.699e-01 5.690e-02 -4.742 2.27e-06 ***
## pos_13_pd -3.427e-01 5.776e-02 -5.932 3.54e-09 ***
## pos_14_pd -3.391e-01 5.988e-02 -5.663 1.71e-08 ***
## pos_15_pd -3.515e-01 6.129e-02 -5.735 1.13e-08 ***
## pos_16_pd -3.731e-01 6.233e-02 -5.987 2.55e-09 ***
## pos_17_pd -3.741e-01 6.473e-02 -5.779 8.79e-09 ***
## pos_18_pd -3.678e-01 6.643e-02 -5.537 3.51e-08 ***
## pos_19_pd -3.599e-01 6.762e-02 -5.322 1.15e-07 ***
## pos_20_pd -3.754e-01 7.048e-02 -5.326 1.12e-07 ***
## pos_21_pd -4.122e-01 7.343e-02 -5.614 2.27e-08 ***
## pos_22_pd -4.150e-01 7.523e-02 -5.517 3.92e-08 ***
## pos_23_pd -4.370e-01 7.719e-02 -5.661 1.73e-08 ***
## pos_24_pd -4.847e-01 8.208e-02 -5.905 4.17e-09 ***
## pos_25_pd -4.491e-01 8.668e-02 -5.181 2.44e-07 ***
## pos_26_pd -4.496e-01 8.775e-02 -5.124 3.30e-07 ***
## pos_27_pd -4.935e-01 8.904e-02 -5.542 3.40e-08 ***
## pos_28_pd -4.711e-01 9.051e-02 -5.205 2.15e-07 ***
## pos_29_pd -4.818e-01 9.857e-02 -4.887 1.11e-06 ***
## pos_30_pd -4.227e-01 1.018e-01 -4.153 3.43e-05 ***
## pos_31_pd -3.879e-01 1.054e-01 -3.682 0.000238 ***
## pos_32_pd -4.492e-01 1.161e-01 -3.870 0.000113 ***
## pos_33_pd -4.813e-01 1.214e-01 -3.964 7.64e-05 ***
## pos_34_pd -4.751e-01 1.227e-01 -3.872 0.000111 ***
## pos_35_pd -6.716e-01 1.426e-01 -4.709 2.66e-06 ***
## pos_36_pd -7.051e-01 1.438e-01 -4.903 1.02e-06 ***
## pos_37_pd -7.306e-01 1.695e-01 -4.310 1.71e-05 ***
## pos_38_pd -6.815e-01 2.272e-01 -2.999 0.002742 **
## pos_39_pd -7.017e-01 2.282e-01 -3.074 0.002139 **
## Time_Period_ID:RegionMidwest 8.691e-02 5.282e-03 16.453 < 2e-16 ***
## Time_Period_ID:RegionNortheast 7.370e-02 6.058e-03 12.165 < 2e-16 ***
## Time_Period_ID:RegionSouth 7.974e-02 4.685e-03 17.022 < 2e-16 ***
## Time_Period_ID:RegionWest 6.430e-02 5.133e-03 12.528 < 2e-16 ***
## RegionMidwest:I(Time_Period_ID^2) -7.645e-04 1.308e-04 -5.846 5.92e-09 ***
## RegionNortheast:I(Time_Period_ID^2) -3.293e-04 1.518e-04 -2.170 0.030138 *
## RegionSouth:I(Time_Period_ID^2) -7.483e-04 1.209e-04 -6.191 7.29e-10 ***
## RegionWest:I(Time_Period_ID^2) -7.087e-04 1.313e-04 -5.397 7.61e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2967 on 1895 degrees of freedom
## Multiple R-squared: 0.8447, Adjusted R-squared: 0.8362
## F-statistic: 99.13 on 104 and 1895 DF, p-value: < 2.2e-16
Sandwich Estimator
#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_lin_time <- model.matrix(sensitivity_anlys_post_tx_model_log_fixed_lin_time)
#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_post_tx_log_fixed_lin_time <- coef(sensitivity_anlys_post_tx_model_log_fixed_lin_time)
sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time <-
compute_sd_and_CI((full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_lin_time),
log(sensitivity_anlys_event_study_data$prop_dead),
coefficient_values_sensitivity_anlys_post_tx_log_fixed_lin_time,
p = ncol(full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_lin_time) - 50)
sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time
## lb_coef coef_values ub_coef
## (Intercept) -1.089784e+01 -1.080161e+01 -1.070539e+01
## StateAlaska 1.377462e-01 2.967280e-01 4.557098e-01
## StateArizona 3.572478e-01 4.986602e-01 6.400727e-01
## StateArkansas -6.645857e-01 -5.590763e-01 -4.535669e-01
## StateCalifornia 8.192892e-02 2.543418e-01 4.267547e-01
## StateColorado 8.411816e-02 2.249102e-01 3.657023e-01
## StateConnecticut -1.274304e-01 1.058193e-01 3.390691e-01
## StateDelaware -6.062897e-02 6.700585e-02 1.946407e-01
## StateFlorida 3.655075e-01 4.732739e-01 5.810402e-01
## StateGeorgia 8.581420e-02 1.861762e-01 2.865383e-01
## StateHawaii -3.790756e-01 -2.335472e-01 -8.801869e-02
## StateIdaho -8.147777e-02 5.990027e-02 2.012783e-01
## StateIllinois -6.146294e-02 1.075467e-01 2.765563e-01
## StateIndiana -2.298681e-01 -8.394337e-02 6.198141e-02
## StateIowa -8.706980e-01 -7.274116e-01 -5.841252e-01
## StateKansas -4.783749e-01 -3.463026e-01 -2.142302e-01
## StateKentucky 5.483942e-01 6.378878e-01 7.273813e-01
## StateLouisiana 3.277501e-01 4.278619e-01 5.279737e-01
## StateMaine -3.088537e-01 -6.923281e-02 1.703881e-01
## StateMaryland -1.611573e+00 -1.409027e+00 -1.206480e+00
## StateMassachusetts -5.388172e-01 -2.044092e-01 1.299989e-01
## StateMichigan -1.985843e-01 -6.756352e-02 6.345722e-02
## StateMinnesota -9.350398e-01 -7.958091e-01 -6.565784e-01
## StateMississippi -2.679502e-01 -1.571042e-01 -4.625827e-02
## StateMissouri -5.911046e-02 6.991381e-02 1.989381e-01
## StateMontana -2.247769e-01 -7.476100e-02 7.525488e-02
## StateNebraska -1.216469e+00 -1.082111e+00 -9.477529e-01
## StateNevada 6.468741e-01 7.919969e-01 9.371197e-01
## StateNew Hampshire -2.404466e-01 -1.481407e-02 2.108185e-01
## StateNew Jersey -1.665574e-01 6.674317e-02 3.000437e-01
## StateNew Mexico 7.068903e-01 8.668822e-01 1.026874e+00
## StateNew York -4.685869e-01 -2.456932e-01 -2.279944e-02
## StateNorth Carolina 1.978452e-01 2.847260e-01 3.716067e-01
## StateNorth Dakota -1.546468e+00 -1.363971e+00 -1.181474e+00
## StateOhio 3.605855e-01 5.174907e-01 6.743959e-01
## StateOklahoma 3.010775e-01 4.108628e-01 5.206481e-01
## StateOregon -2.016273e-01 -6.070866e-02 8.020998e-02
## StatePennsylvania 4.223253e-01 6.254850e-01 8.286446e-01
## StateRhode Island -9.035257e-01 -5.083039e-01 -1.130821e-01
## StateSouth Carolina -1.049984e-02 8.840328e-02 1.873064e-01
## StateSouth Dakota -1.456686e+00 -1.295833e+00 -1.134980e+00
## StateTennessee 3.811316e-01 4.656090e-01 5.500865e-01
## StateTexas 2.771875e-02 1.433278e-01 2.589369e-01
## StateUtah 3.872767e-02 2.650449e-01 4.913622e-01
## StateVermont -5.901314e-01 -3.443276e-01 -9.852372e-02
## StateVirginia -2.766106e-02 6.727204e-02 1.622051e-01
## StateWashington 1.419634e-01 2.841846e-01 4.264057e-01
## StateWest Virginia 5.765619e-01 7.170779e-01 8.575938e-01
## StateWisconsin -1.786456e-01 -5.121088e-02 7.622383e-02
## StateWyoming 9.222745e-02 2.618196e-01 4.314117e-01
## Naloxone_Pharmacy_Yes_Redefined -3.675226e-03 5.810410e-02 1.198834e-01
## Naloxone_Pharmacy_No_Redefined -4.544605e-02 1.576258e-02 7.697122e-02
## Medical_Marijuana_Redefined 1.514954e-01 2.221351e-01 2.927748e-01
## Recreational_Marijuana_Redefined -1.458147e-01 -7.030772e-02 5.199212e-03
## GSL_Redefined 7.240317e-03 5.969397e-02 1.121476e-01
## PDMP_Redefined -2.356820e-01 -1.831820e-01 -1.306820e-01
## Medicaid_Expansion_Redefined 2.548103e-02 7.554247e-02 1.256039e-01
## pos_0_pd -1.232220e-01 -4.391484e-02 3.539236e-02
## pos_1_pd -1.753316e-01 -8.451575e-02 6.300065e-03
## pos_2_pd -1.345725e-01 -5.723292e-02 2.010664e-02
## pos_3_pd -1.767463e-01 -9.707618e-02 -1.740610e-02
## pos_4_pd -1.864027e-01 -1.060528e-01 -2.570288e-02
## pos_5_pd -2.338331e-01 -1.505587e-01 -6.728426e-02
## pos_6_pd -2.431210e-01 -1.542152e-01 -6.530942e-02
## pos_7_pd -2.484738e-01 -1.543273e-01 -6.018072e-02
## pos_8_pd -3.019100e-01 -2.136631e-01 -1.254163e-01
## pos_9_pd -3.339051e-01 -2.372509e-01 -1.405966e-01
## pos_10_pd -3.551988e-01 -2.553866e-01 -1.555745e-01
## pos_11_pd -3.537798e-01 -2.633042e-01 -1.728287e-01
## pos_12_pd -3.681921e-01 -2.698599e-01 -1.715278e-01
## pos_13_pd -4.602296e-01 -3.426755e-01 -2.251215e-01
## pos_14_pd -4.594010e-01 -3.390926e-01 -2.187843e-01
## pos_15_pd -4.618573e-01 -3.515039e-01 -2.411505e-01
## pos_16_pd -4.903779e-01 -3.731365e-01 -2.558951e-01
## pos_17_pd -4.941843e-01 -3.740702e-01 -2.539562e-01
## pos_18_pd -4.878219e-01 -3.678096e-01 -2.477973e-01
## pos_19_pd -4.749640e-01 -3.599141e-01 -2.448642e-01
## pos_20_pd -4.986432e-01 -3.754216e-01 -2.522001e-01
## pos_21_pd -5.463634e-01 -4.122110e-01 -2.780585e-01
## pos_22_pd -5.478495e-01 -4.150284e-01 -2.822073e-01
## pos_23_pd -5.794203e-01 -4.369711e-01 -2.945219e-01
## pos_24_pd -6.367526e-01 -4.846949e-01 -3.326372e-01
## pos_25_pd -6.223804e-01 -4.491097e-01 -2.758390e-01
## pos_26_pd -6.176132e-01 -4.496148e-01 -2.816163e-01
## pos_27_pd -6.721251e-01 -4.934802e-01 -3.148352e-01
## pos_28_pd -6.582506e-01 -4.710687e-01 -2.838869e-01
## pos_29_pd -6.826784e-01 -4.817697e-01 -2.808610e-01
## pos_30_pd -6.304967e-01 -4.227249e-01 -2.149530e-01
## pos_31_pd -6.222924e-01 -3.878906e-01 -1.534888e-01
## pos_32_pd -6.725618e-01 -4.492206e-01 -2.258793e-01
## pos_33_pd -7.607229e-01 -4.813352e-01 -2.019476e-01
## pos_34_pd -7.603424e-01 -4.751498e-01 -1.899573e-01
## pos_35_pd -9.116375e-01 -6.715534e-01 -4.314694e-01
## pos_36_pd -9.468931e-01 -7.050687e-01 -4.632442e-01
## pos_37_pd -9.597621e-01 -7.305666e-01 -5.013711e-01
## pos_38_pd -8.739929e-01 -6.815169e-01 -4.890408e-01
## pos_39_pd -9.575988e-01 -7.016723e-01 -4.457458e-01
## Time_Period_ID:RegionMidwest 7.736058e-02 8.691258e-02 9.646458e-02
## Time_Period_ID:RegionNortheast 5.286972e-02 7.369820e-02 9.452667e-02
## Time_Period_ID:RegionSouth 7.141658e-02 7.974451e-02 8.807245e-02
## Time_Period_ID:RegionWest 5.475924e-02 6.430477e-02 7.385029e-02
## RegionMidwest:I(Time_Period_ID^2) -9.870165e-04 -7.645227e-04 -5.420290e-04
## RegionNortheast:I(Time_Period_ID^2) -7.629619e-04 -3.292992e-04 1.043635e-04
## RegionSouth:I(Time_Period_ID^2) -9.583733e-04 -7.482645e-04 -5.381557e-04
## RegionWest:I(Time_Period_ID^2) -9.404291e-04 -7.087475e-04 -4.770660e-04
## sd_coef
## (Intercept) 0.0490957400
## StateAlaska 0.0811131627
## StateArizona 0.0721492324
## StateArkansas 0.0538313336
## StateCalifornia 0.0879657491
## StateColorado 0.0718326767
## StateConnecticut 0.1190049832
## StateDelaware 0.0651198065
## StateFlorida 0.0549828165
## StateGeorgia 0.0512051164
## StateHawaii 0.0742492201
## StateIdaho 0.0721316506
## StateIllinois 0.0862293965
## StateIndiana 0.0744514193
## StateIowa 0.0731052897
## StateKansas 0.0673838653
## StateKentucky 0.0456599777
## StateLouisiana 0.0510774544
## StateMaine 0.1222555731
## StateMaryland 0.1033398255
## StateMassachusetts 0.1706163396
## StateMichigan 0.0668473155
## StateMinnesota 0.0710360630
## StateMississippi 0.0565540664
## StateMissouri 0.0658287065
## StateMontana 0.0765387171
## StateNebraska 0.0685499310
## StateNevada 0.0740422480
## StateNew Hampshire 0.1151186308
## StateNew Jersey 0.1190308921
## StateNew Mexico 0.0816284883
## StateNew York 0.1137212858
## StateNorth Carolina 0.0443269227
## StateNorth Dakota 0.0931106490
## StateOhio 0.0800536790
## StateOklahoma 0.0560129333
## StateOregon 0.0718972637
## StatePennsylvania 0.1036528910
## StateRhode Island 0.2016437652
## StateSouth Carolina 0.0504607762
## StateSouth Dakota 0.0820679025
## StateTennessee 0.0431007348
## StateTexas 0.0589842209
## StateUtah 0.1154679802
## StateVermont 0.1254101229
## StateVirginia 0.0484352568
## StateWashington 0.0725617948
## StateWest Virginia 0.0716918186
## StateWisconsin 0.0650177061
## StateWyoming 0.0865265942
## Naloxone_Pharmacy_Yes_Redefined 0.0315200643
## Naloxone_Pharmacy_No_Redefined 0.0312288969
## Medical_Marijuana_Redefined 0.0360406637
## Recreational_Marijuana_Redefined 0.0385239472
## GSL_Redefined 0.0267620668
## PDMP_Redefined 0.0267857235
## Medicaid_Expansion_Redefined 0.0255415494
## pos_0_pd 0.0404628545
## pos_1_pd 0.0463346019
## pos_2_pd 0.0394589631
## pos_3_pd 0.0406479982
## pos_4_pd 0.0409948418
## pos_5_pd 0.0424869393
## pos_6_pd 0.0453600901
## pos_7_pd 0.0480339467
## pos_8_pd 0.0450239010
## pos_9_pd 0.0493133927
## pos_10_pd 0.0509245689
## pos_11_pd 0.0461609957
## pos_12_pd 0.0501694689
## pos_13_pd 0.0599765576
## pos_14_pd 0.0613818152
## pos_15_pd 0.0563027514
## pos_16_pd 0.0598170316
## pos_17_pd 0.0612826655
## pos_18_pd 0.0612307741
## pos_19_pd 0.0586989247
## pos_20_pd 0.0628681264
## pos_21_pd 0.0684451285
## pos_22_pd 0.0677658707
## pos_23_pd 0.0726781649
## pos_24_pd 0.0775804629
## pos_25_pd 0.0884034189
## pos_26_pd 0.0857135144
## pos_27_pd 0.0911453894
## pos_28_pd 0.0955009363
## pos_29_pd 0.1025044471
## pos_30_pd 0.1060060398
## pos_31_pd 0.1195927353
## pos_32_pd 0.1139496052
## pos_33_pd 0.1425447070
## pos_34_pd 0.1455064070
## pos_35_pd 0.1224918631
## pos_36_pd 0.1233798189
## pos_37_pd 0.1169364617
## pos_38_pd 0.0982020642
## pos_39_pd 0.1305747399
## Time_Period_ID:RegionMidwest 0.0048734711
## Time_Period_ID:RegionNortheast 0.0106267742
## Time_Period_ID:RegionSouth 0.0042489462
## Time_Period_ID:RegionWest 0.0048701665
## RegionMidwest:I(Time_Period_ID^2) 0.0001135172
## RegionNortheast:I(Time_Period_ID^2) 0.0002212565
## RegionSouth:I(Time_Period_ID^2) 0.0001071984
## RegionWest:I(Time_Period_ID^2) 0.0001182049
Plot Results
#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx_log_fixed_lin_time <- sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time %>%
mutate(term = rownames(sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time)) %>%
dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
filter(term %in% c(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_post_tx_log_fixed_lin_time) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx_log_fixed_lin_time$num_states <- sapply(plot_post_tx_log_fixed_lin_time$term, function(x){sum(sensitivity_anlys_event_study_data[,x])})
dwplot(plot_post_tx_log_fixed_lin_time, colour = "black",
vars_order = c(sapply(((max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0),
function(x){paste("pos_", x, "_pd", sep = "")}))) +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black"),
axis.text.x = element_text(angle = 45, size = 4)) +
geom_vline(aes(xintercept = 0), linetype = "dashed") +
labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals",
title = "Coefficient of Pre-Intervention and Post-Intervention Periods") +
scale_color_grey() +
coord_flip()
# geom_vline(aes(xintercept = coef(main_analysis_model_log_fixed_lin_time)["Intervention_Redefined"]),
# linetype = "dashed", color = "red")
# geom_text(aes(label = paste("Coefficient Estimate: ", coef(main_analysis_model_log_fixed_lin_time)["Intervention_Redefined"]), y = 12,
# x = coef(main_analysis_model_log_fixed_lin_time)["Intervention_Redefined"] + 0.1), color = "red")
# geom_text(aes(label = num_states, x = .1, y = 40:1), size = 2)
Attributable Deaths
date_data <- sensitivity_anlys_event_study_data[, c("Time_Period_ID", "Time_Period_Start")]
date_data <- date_data[!duplicated(date_data),]
attr_deaths_est_log_lin_time_diff_post_tx <- attr_death_compute(sensitivity_anlys_event_study_data,
sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time,
post_tx_model = TRUE)
attr_deaths_est_log_lin_time_diff_post_tx <- merge(attr_deaths_est_log_lin_time_diff_post_tx, date_data,
by.x = "Time_Period", by.y = "Time_Period_ID")
ggplot(attr_deaths_est_log_lin_time_diff_post_tx, aes(x = Time_Period_Start)) +
# geom_point(aes(y = attr_deaths)) +
geom_line(aes(y = attr_deaths, linetype = "Estimate")) +
# geom_point(aes(y = attr_deaths_lb)) +
geom_line(aes(y = attr_deaths_lb, linetype = "95% CI")) +
# geom_point(aes(y = attr_deaths_ub)) +
geom_line(aes(y = attr_deaths_ub, linetype = "95% CI")) +
labs(x = "Date", y = "Attributable Deaths",
title = "Estimated Number of Attributable Deaths Using Linear and Quad. Time Effects,
Log Probability of Drug Overdose Death, Linear Policy Effects",
linetype = "") +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black")) +
scale_linetype_manual(values = c("dashed", "solid"))
Analysis With Only Periods After Treatment with Model SD
summary_model_log_fixed_lin_time_post_tx_model_sd <- summary(sensitivity_anlys_post_tx_model_log_fixed_lin_time)
coef_log_fixed_lin_time_post_tx_model_sd <- data.frame(coef_values = summary_model_log_fixed_lin_time_post_tx_model_sd$coefficients[,1],
lb_coef = summary_model_log_fixed_lin_time_post_tx_model_sd$coefficients[,1] -
1.96*summary_model_log_fixed_lin_time_post_tx_model_sd$coefficients[,2],
ub_coef = summary_model_log_fixed_lin_time_post_tx_model_sd$coefficients[,1] +
1.96*summary_model_log_fixed_lin_time_post_tx_model_sd$coefficients[,2])
Plot Results
#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx_log_fixed_lin_time_model_sd <- coef_log_fixed_lin_time_post_tx_model_sd %>%
mutate(term = rownames(coef_log_fixed_lin_time_post_tx_model_sd)) %>%
dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
filter(term %in% c(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_post_tx_log_fixed_lin_time_model_sd) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx_log_fixed_lin_time_model_sd$num_states <- sapply(plot_post_tx_log_fixed_lin_time_model_sd$term, function(x){sum(sensitivity_anlys_event_study_data[,x])})
dwplot(plot_post_tx_log_fixed_lin_time_model_sd, colour = "black",
vars_order = c(sapply(((max(merged_main_time_data_int$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0),
function(x){paste("pos_", x, "_pd", sep = "")}))) +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black"),
axis.text.x = element_text(angle = 45, size = 4)) +
geom_vline(aes(xintercept = 0), linetype = "dashed") +
labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals",
title = "Coefficient of Pre-Intervention and Post-Intervention Periods") +
scale_color_grey() +
coord_flip() +
geom_vline(aes(xintercept = coef(main_analysis_model_log_fixed_lin_time)["Intervention_Redefined"]),
linetype = "dashed", color = "red") +
geom_text(aes(label = paste("Coefficient Estimate: ", coef(main_analysis_model_log_fixed_lin_time)["Intervention_Redefined"]), y = 12,
x = coef(main_analysis_model_log_fixed_lin_time)["Intervention_Redefined"] + 0.1), color = "red")
# geom_text(aes(label = num_states, x = .1, y = 40:1), size = 2)
Analysis With Only Periods After Treatment Subset
formula_post_tx_log_fixed_lin_time <- formula(paste("log(prop_dead)~ State +
Time_Period_ID:Region +
I(Time_Period_ID^2):Region +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +",
paste(sapply(0:(29 -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_post_tx_model_log_fixed_lin_time_subset<-lm(formula_post_tx_log_fixed_lin_time,
data = data_subset)
summary(sensitivity_anlys_post_tx_model_log_fixed_lin_time_subset)
##
## Call:
## lm(formula = formula_post_tx_log_fixed_lin_time, data = data_subset)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.95559 -0.12809 0.00672 0.14870 1.08300
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.091e+01 7.112e-02 -153.373 < 2e-16 ***
## StateAlaska 4.274e-01 1.082e-01 3.948 8.27e-05 ***
## StateArizona 6.058e-01 1.027e-01 5.896 4.70e-09 ***
## StateArkansas -5.290e-01 8.071e-02 -6.555 7.91e-11 ***
## StateCalifornia 4.080e-01 1.133e-01 3.599 0.000330 ***
## StateColorado 3.136e-01 1.078e-01 2.910 0.003675 **
## StateConnecticut 1.860e-01 1.110e-01 1.676 0.094028 .
## StateDelaware 7.298e-02 8.169e-02 0.893 0.371820
## StateFlorida 5.434e-01 8.480e-02 6.408 2.03e-10 ***
## StateGeorgia 2.321e-01 8.730e-02 2.658 0.007943 **
## StateHawaii -1.280e-01 1.078e-01 -1.187 0.235427
## StateIdaho 1.331e-01 1.045e-01 1.274 0.202961
## StateIllinois 3.728e-01 1.079e-01 3.457 0.000564 ***
## StateIndiana -7.394e-02 1.042e-01 -0.709 0.478242
## StateIowa -6.737e-01 1.039e-01 -6.485 1.24e-10 ***
## StateKansas -2.381e-01 1.032e-01 -2.308 0.021175 *
## StateKentucky 7.202e-01 8.074e-02 8.920 < 2e-16 ***
## StateLouisiana 4.539e-01 8.056e-02 5.635 2.13e-08 ***
## StateMaine -1.110e-01 1.123e-01 -0.988 0.323235
## StateMaryland -1.668e+00 8.458e-02 -19.717 < 2e-16 ***
## StateMassachusetts -3.474e-01 1.085e-01 -3.202 0.001395 **
## StateMichigan 5.662e-03 1.047e-01 0.054 0.956866
## StateMinnesota -6.910e-01 1.064e-01 -6.497 1.15e-10 ***
## StateMississippi -1.118e-02 8.047e-02 -0.139 0.889558
## StateMissouri 1.442e-01 1.046e-01 1.379 0.168134
## StateMontana -8.668e-04 1.064e-01 -0.008 0.993499
## StateNebraska -9.949e-01 1.046e-01 -9.511 < 2e-16 ***
## StateNevada 9.338e-01 1.074e-01 8.697 < 2e-16 ***
## StateNew Hampshire -9.882e-02 1.088e-01 -0.909 0.363676
## StateNew Jersey 7.787e-02 1.111e-01 0.701 0.483460
## StateNew Mexico 1.095e+00 1.109e-01 9.877 < 2e-16 ***
## StateNew York -1.430e-01 1.098e-01 -1.302 0.193240
## StateNorth Carolina 3.184e-01 8.021e-02 3.969 7.58e-05 ***
## StateNorth Dakota -1.353e+00 1.042e-01 -12.985 < 2e-16 ***
## StateOhio 5.141e-01 1.085e-01 4.738 2.38e-06 ***
## StateOklahoma 5.687e-01 8.039e-02 7.074 2.41e-12 ***
## StateOregon 4.517e-02 1.076e-01 0.420 0.674651
## StatePennsylvania 6.673e-01 1.135e-01 5.880 5.17e-09 ***
## StateRhode Island -6.474e-01 1.097e-01 -5.902 4.54e-09 ***
## StateSouth Carolina 1.539e-01 8.050e-02 1.912 0.056077 .
## StateSouth Dakota -1.220e+00 1.048e-01 -11.639 < 2e-16 ***
## StateTennessee 4.655e-01 7.933e-02 5.868 5.53e-09 ***
## StateTexas 2.892e-01 8.417e-02 3.435 0.000609 ***
## StateUtah 1.571e-01 1.048e-01 1.499 0.134152
## StateVermont -2.941e-01 1.095e-01 -2.687 0.007304 **
## StateVirginia 7.035e-02 8.128e-02 0.865 0.386951
## StateWashington 4.252e-01 1.084e-01 3.922 9.24e-05 ***
## StateWest Virginia 7.256e-01 8.082e-02 8.977 < 2e-16 ***
## StateWisconsin -2.257e-02 1.043e-01 -0.216 0.828759
## StateWyoming 2.713e-01 1.032e-01 2.628 0.008678 **
## Naloxone_Pharmacy_Yes_Redefined -2.196e-01 8.264e-02 -2.657 0.007983 **
## Naloxone_Pharmacy_No_Redefined -5.699e-02 5.770e-02 -0.988 0.323514
## Medical_Marijuana_Redefined 2.086e-01 4.261e-02 4.896 1.10e-06 ***
## Recreational_Marijuana_Redefined -1.168e-01 1.470e-01 -0.794 0.427066
## GSL_Redefined 6.460e-02 5.194e-02 1.244 0.213825
## PDMP_Redefined -1.947e-01 2.904e-02 -6.703 2.99e-11 ***
## Medicaid_Expansion_Redefined -5.890e-03 5.491e-02 -0.107 0.914591
## pos_0_pd -2.189e-02 5.020e-02 -0.436 0.662773
## pos_1_pd -9.194e-02 5.114e-02 -1.798 0.072462 .
## pos_2_pd -5.145e-02 5.171e-02 -0.995 0.319958
## pos_3_pd -1.057e-01 5.395e-02 -1.959 0.050289 .
## pos_4_pd -1.077e-01 5.524e-02 -1.949 0.051469 .
## pos_5_pd -1.383e-01 5.631e-02 -2.457 0.014145 *
## pos_6_pd -1.596e-01 5.854e-02 -2.726 0.006484 **
## pos_7_pd -1.415e-01 5.990e-02 -2.362 0.018309 *
## pos_8_pd -1.719e-01 6.097e-02 -2.820 0.004877 **
## pos_9_pd -2.089e-01 6.408e-02 -3.260 0.001144 **
## pos_10_pd -2.369e-01 6.715e-02 -3.528 0.000433 ***
## pos_11_pd -2.205e-01 6.875e-02 -3.208 0.001369 **
## pos_12_pd -2.408e-01 7.062e-02 -3.409 0.000670 ***
## pos_13_pd -3.672e-01 7.589e-02 -4.839 1.46e-06 ***
## pos_14_pd -3.699e-01 8.075e-02 -4.582 5.04e-06 ***
## pos_15_pd -2.912e-01 8.176e-02 -3.562 0.000381 ***
## pos_16_pd -3.257e-01 8.293e-02 -3.928 9.00e-05 ***
## pos_17_pd -3.436e-01 8.422e-02 -4.080 4.77e-05 ***
## pos_18_pd -3.463e-01 9.277e-02 -3.732 0.000197 ***
## pos_19_pd -3.135e-01 9.645e-02 -3.251 0.001180 **
## pos_20_pd -3.141e-01 1.001e-01 -3.137 0.001744 **
## pos_21_pd -3.555e-01 1.119e-01 -3.179 0.001513 **
## pos_22_pd -3.704e-01 1.182e-01 -3.135 0.001757 **
## pos_23_pd -4.075e-01 1.207e-01 -3.375 0.000759 ***
## pos_24_pd -5.288e-01 1.401e-01 -3.776 0.000166 ***
## pos_25_pd -5.278e-01 1.418e-01 -3.723 0.000205 ***
## pos_26_pd -4.619e-01 1.683e-01 -2.745 0.006125 **
## pos_27_pd -4.197e-01 2.287e-01 -1.835 0.066675 .
## pos_28_pd -2.417e-01 2.324e-01 -1.040 0.298510
## Time_Period_ID:RegionMidwest 9.416e-02 8.216e-03 11.461 < 2e-16 ***
## Time_Period_ID:RegionNortheast 1.020e-01 9.695e-03 10.516 < 2e-16 ***
## Time_Period_ID:RegionSouth 9.537e-02 7.201e-03 13.245 < 2e-16 ***
## Time_Period_ID:RegionWest 6.822e-02 8.059e-03 8.466 < 2e-16 ***
## RegionMidwest:I(Time_Period_ID^2) -1.007e-03 2.684e-04 -3.752 0.000183 ***
## RegionNortheast:I(Time_Period_ID^2) -1.307e-03 3.224e-04 -4.055 5.30e-05 ***
## RegionSouth:I(Time_Period_ID^2) -1.301e-03 2.341e-04 -5.557 3.30e-08 ***
## RegionWest:I(Time_Period_ID^2) -7.723e-04 2.652e-04 -2.912 0.003647 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3015 on 1356 degrees of freedom
## Multiple R-squared: 0.8225, Adjusted R-squared: 0.8104
## F-statistic: 67.58 on 93 and 1356 DF, p-value: < 2.2e-16
Sandwich Estimator
#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_lin_time_subset <-
model.matrix(sensitivity_anlys_post_tx_model_log_fixed_lin_time_subset)
#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_post_tx_log_fixed_lin_time_subset <- coef(sensitivity_anlys_post_tx_model_log_fixed_lin_time_subset)
sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time_subset <-
compute_sd_and_CI((full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_lin_time_subset),
log(data_subset$prop_dead),
coefficient_values_sensitivity_anlys_post_tx_log_fixed_lin_time_subset,
p = ncol(full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_lin_time_subset) - 50)
sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time_subset
## lb_coef coef_values ub_coef
## (Intercept) -11.023282693 -1.090742e+01 -1.079156e+01
## StateAlaska 0.235133487 4.273972e-01 6.196609e-01
## StateArizona 0.437914755 6.057654e-01 7.736160e-01
## StateArkansas -0.667087310 -5.290018e-01 -3.909163e-01
## StateCalifornia 0.195843512 4.079544e-01 6.200652e-01
## StateColorado 0.143067848 3.136282e-01 4.841886e-01
## StateConnecticut -0.093702482 1.859977e-01 4.656978e-01
## StateDelaware -0.073053160 7.297514e-02 2.190034e-01
## StateFlorida 0.416674394 5.433858e-01 6.700972e-01
## StateGeorgia 0.107944895 2.320893e-01 3.562337e-01
## StateHawaii -0.302227812 -1.279554e-01 4.631692e-02
## StateIdaho -0.037281975 1.330894e-01 3.034608e-01
## StateIllinois 0.189126809 3.728130e-01 5.564992e-01
## StateIndiana -0.242052887 -7.393566e-02 9.418157e-02
## StateIowa -0.845782838 -6.736635e-01 -5.015441e-01
## StateKansas -0.393312824 -2.380811e-01 -8.284935e-02
## StateKentucky 0.610068000 7.201852e-01 8.303024e-01
## StateLouisiana 0.328483962 4.539403e-01 5.793965e-01
## StateMaine -0.395633347 -1.109917e-01 1.736500e-01
## StateMaryland -1.864276094 -1.667625e+00 -1.470974e+00
## StateMassachusetts -0.725762517 -3.474105e-01 3.094145e-02
## StateMichigan -0.149674005 5.662479e-03 1.609990e-01
## StateMinnesota -0.857653068 -6.909765e-01 -5.243000e-01
## StateMississippi -0.127799183 -1.117615e-02 1.054469e-01
## StateMissouri -0.003744441 1.442237e-01 2.921917e-01
## StateMontana -0.173522996 -8.668399e-04 1.717893e-01
## StateNebraska -1.153801789 -9.949016e-01 -8.360015e-01
## StateNevada 0.763365368 9.337537e-01 1.104142e+00
## StateNew Hampshire -0.355206774 -9.882452e-02 1.575577e-01
## StateNew Jersey -0.210474548 7.787446e-02 3.662235e-01
## StateNew Mexico 0.894942772 1.095285e+00 1.295628e+00
## StateNew York -0.406006599 -1.429667e-01 1.200732e-01
## StateNorth Carolina 0.215166203 3.183710e-01 4.215758e-01
## StateNorth Dakota -1.586142779 -1.353422e+00 -1.120701e+00
## StateOhio 0.330259428 5.141044e-01 6.979494e-01
## StateOklahoma 0.459256321 5.686696e-01 6.780828e-01
## StateOregon -0.124807899 4.516508e-02 2.151381e-01
## StatePennsylvania 0.414552073 6.672716e-01 9.199911e-01
## StateRhode Island -1.111525296 -6.473864e-01 -1.832475e-01
## StateSouth Carolina 0.035379721 1.539228e-01 2.724658e-01
## StateSouth Dakota -1.406996687 -1.219749e+00 -1.032501e+00
## StateTennessee 0.360290983 4.655087e-01 5.707264e-01
## StateTexas 0.163471204 2.891574e-01 4.148436e-01
## StateUtah -0.092235213 1.571495e-01 4.065341e-01
## StateVermont -0.581440694 -2.941311e-01 -6.821537e-03
## StateVirginia -0.048848333 7.034543e-02 1.895392e-01
## StateWashington 0.253603664 4.252324e-01 5.968611e-01
## StateWest Virginia 0.546578326 7.255767e-01 9.045750e-01
## StateWisconsin -0.173940655 -2.256830e-02 1.288040e-01
## StateWyoming 0.077279857 2.712827e-01 4.652855e-01
## Naloxone_Pharmacy_Yes_Redefined -0.326260650 -2.195564e-01 -1.128522e-01
## Naloxone_Pharmacy_No_Redefined -0.176146117 -5.698786e-02 6.217040e-02
## Medical_Marijuana_Redefined 0.100694356 2.085979e-01 3.165014e-01
## Recreational_Marijuana_Redefined -0.255121399 -1.167887e-01 2.154391e-02
## GSL_Redefined -0.036003519 6.460321e-02 1.652099e-01
## PDMP_Redefined -0.249753144 -1.946791e-01 -1.396051e-01
## Medicaid_Expansion_Redefined -0.101143723 -5.890220e-03 8.936328e-02
## pos_0_pd -0.110293146 -2.189486e-02 6.650342e-02
## pos_1_pd -0.189497204 -9.193815e-02 5.620896e-03
## pos_2_pd -0.131970698 -5.144947e-02 2.907176e-02
## pos_3_pd -0.187587554 -1.057042e-01 -2.382087e-02
## pos_4_pd -0.186343571 -1.076845e-01 -2.902539e-02
## pos_5_pd -0.225007960 -1.383359e-01 -5.166387e-02
## pos_6_pd -0.254856094 -1.595957e-01 -6.433526e-02
## pos_7_pd -0.243459495 -1.414953e-01 -3.953115e-02
## pos_8_pd -0.265077022 -1.719037e-01 -7.873044e-02
## pos_9_pd -0.316981488 -2.088760e-01 -1.007705e-01
## pos_10_pd -0.353466894 -2.368807e-01 -1.202946e-01
## pos_11_pd -0.326600183 -2.205425e-01 -1.144847e-01
## pos_12_pd -0.364619662 -2.407627e-01 -1.169057e-01
## pos_13_pd -0.537125144 -3.671995e-01 -1.972739e-01
## pos_14_pd -0.551658895 -3.699445e-01 -1.882301e-01
## pos_15_pd -0.418529692 -2.912092e-01 -1.638887e-01
## pos_16_pd -0.467576839 -3.257402e-01 -1.839035e-01
## pos_17_pd -0.493181543 -3.435766e-01 -1.939717e-01
## pos_18_pd -0.510248067 -3.462708e-01 -1.822935e-01
## pos_19_pd -0.473693631 -3.135105e-01 -1.533274e-01
## pos_20_pd -0.491357096 -3.141007e-01 -1.368444e-01
## pos_21_pd -0.591164622 -3.555464e-01 -1.199282e-01
## pos_22_pd -0.633488273 -3.703993e-01 -1.073104e-01
## pos_23_pd -0.659211093 -4.074668e-01 -1.557224e-01
## pos_24_pd -0.735178991 -5.288245e-01 -3.224701e-01
## pos_25_pd -0.732526295 -5.278271e-01 -3.231279e-01
## pos_26_pd -0.719857242 -4.619416e-01 -2.040259e-01
## pos_27_pd -0.639431412 -4.196951e-01 -1.999588e-01
## pos_28_pd -0.447287370 -2.417102e-01 -3.613312e-02
## Time_Period_ID:RegionMidwest 0.080338552 9.415909e-02 1.079796e-01
## Time_Period_ID:RegionNortheast 0.069818688 1.019535e-01 1.340884e-01
## Time_Period_ID:RegionSouth 0.083574420 9.536909e-02 1.071638e-01
## Time_Period_ID:RegionWest 0.053542316 6.822423e-02 8.290614e-02
## RegionMidwest:I(Time_Period_ID^2) -0.001451647 -1.007126e-03 -5.626048e-04
## RegionNortheast:I(Time_Period_ID^2) -0.002291061 -1.307197e-03 -3.233335e-04
## RegionSouth:I(Time_Period_ID^2) -0.001659722 -1.300744e-03 -9.417655e-04
## RegionWest:I(Time_Period_ID^2) -0.001261285 -7.722850e-04 -2.832846e-04
## sd_coef
## (Intercept) 0.0591125963
## StateAlaska 0.0980937358
## StateArizona 0.0856380746
## StateArkansas 0.0704517920
## StateCalifornia 0.1082198212
## StateColorado 0.0870205879
## StateConnecticut 0.1427041563
## StateDelaware 0.0745042337
## StateFlorida 0.0646486677
## StateGeorgia 0.0633389907
## StateHawaii 0.0889144717
## StateIdaho 0.0869241826
## StateIllinois 0.0937174383
## StateIndiana 0.0857740957
## StateIowa 0.0878160113
## StateKansas 0.0791998658
## StateKentucky 0.0561822461
## StateLouisiana 0.0640083118
## StateMaine 0.1452253463
## StateMaryland 0.1003322239
## StateMassachusetts 0.1930367266
## StateMichigan 0.0792533080
## StateMinnesota 0.0850390486
## StateMississippi 0.0595015478
## StateMissouri 0.0754939251
## StateMontana 0.0880898755
## StateNebraska 0.0810715098
## StateNevada 0.0869328287
## StateNew Hampshire 0.1308072714
## StateNew Jersey 0.1471168423
## StateNew Mexico 0.1022155002
## StateNew York 0.1342040191
## StateNorth Carolina 0.0526555213
## StateNorth Dakota 0.1187351952
## StateOhio 0.0937984719
## StateOklahoma 0.0558230933
## StateOregon 0.0867209075
## StatePennsylvania 0.1289385229
## StateRhode Island 0.2368055524
## StateSouth Carolina 0.0604811417
## StateSouth Dakota 0.0955345685
## StateTennessee 0.0536825146
## StateTexas 0.0641256209
## StateUtah 0.1272370778
## StateVermont 0.1465865198
## StateVirginia 0.0608131420
## StateWashington 0.0875656638
## StateWest Virginia 0.0913256806
## StateWisconsin 0.0772307909
## StateWyoming 0.0989810256
## Naloxone_Pharmacy_Yes_Redefined 0.0544409262
## Naloxone_Pharmacy_No_Redefined 0.0607950298
## Medical_Marijuana_Redefined 0.0550528231
## Recreational_Marijuana_Redefined 0.0705778840
## GSL_Redefined 0.0513299618
## PDMP_Redefined 0.0280989900
## Medicaid_Expansion_Redefined 0.0485987258
## pos_0_pd 0.0451011650
## pos_1_pd 0.0497750254
## pos_2_pd 0.0410822608
## pos_3_pd 0.0417772160
## pos_4_pd 0.0401321892
## pos_5_pd 0.0442204321
## pos_6_pd 0.0486022545
## pos_7_pd 0.0520225363
## pos_8_pd 0.0475373944
## pos_9_pd 0.0551558564
## pos_10_pd 0.0594827329
## pos_11_pd 0.0541110882
## pos_12_pd 0.0631923413
## pos_13_pd 0.0866967517
## pos_14_pd 0.0927114176
## pos_15_pd 0.0649594367
## pos_16_pd 0.0723656426
## pos_17_pd 0.0763290368
## pos_18_pd 0.0836618714
## pos_19_pd 0.0817260892
## pos_20_pd 0.0904369243
## pos_21_pd 0.1202133702
## pos_22_pd 0.1342290536
## pos_23_pd 0.1284409881
## pos_24_pd 0.1052828919
## pos_25_pd 0.1044383616
## pos_26_pd 0.1315896356
## pos_27_pd 0.1121103525
## pos_28_pd 0.1048862874
## Time_Period_ID:RegionMidwest 0.0070512967
## Time_Period_ID:RegionNortheast 0.0163953295
## Time_Period_ID:RegionSouth 0.0060176879
## Time_Period_ID:RegionWest 0.0074907706
## RegionMidwest:I(Time_Period_ID^2) 0.0002267965
## RegionNortheast:I(Time_Period_ID^2) 0.0005019713
## RegionSouth:I(Time_Period_ID^2) 0.0001831521
## RegionWest:I(Time_Period_ID^2) 0.0002494900
Plot Results
#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx_log_fixed_lin_time_subset <- sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time_subset %>%
mutate(term = rownames(sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time_subset)) %>%
dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
filter(term %in% c(sapply(0:(max(data_subset$Time_Period_ID) -
min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_post_tx_log_fixed_lin_time_subset) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx_log_fixed_lin_time_subset$num_states_subset <- sapply(plot_post_tx_log_fixed_lin_time_subset$term, function(x){sum(sensitivity_anlys_event_study_data[,x])})
plot_post_tx_data_lin_time <- merge(plot_post_tx_log_fixed_lin_time, plot_post_tx_log_fixed_lin_time_subset,
by = "term", all.x = TRUE)
plot_post_tx_data_lin_time$term <- factor(plot_post_tx_data_lin_time$term,
levels = sapply(0:39, function(x){paste("pos_", x, "_pd", sep = "")}))
ggplot(plot_post_tx_data_lin_time, aes(x = term)) +
geom_point(plot_post_tx_data_lin_time, mapping = aes(y = estimate.y, color = "subset data")) +
geom_pointrange(plot_post_tx_data_lin_time,
mapping = aes(x = term, y = estimate.y, ymin = conf.low.y, ymax = conf.high.y, color = "subset data"),
fatten = 1, alpha = .5) +
geom_point(plot_post_tx_data_lin_time, mapping = aes(y = estimate.x, color = "full data")) +
geom_pointrange(plot_post_tx_data_lin_time,
mapping = aes(x = term, y = estimate.x, ymin = conf.low.x, ymax = conf.high.x, color = "full data"),
fatten = 1, alpha = .5) +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
panel.background = element_blank(), axis.line = element_line(colour = "black"),
axis.text.x = element_text(angle = 45, size = 4),
legend.position = "bottom") +
geom_hline(aes(yintercept = 0), linetype = "dashed") +
labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals",
title = "Coefficient of Pre-Intervention and Post-Intervention Periods",
color = "Full Data or Subset Times")
Analysis With Only Periods After Treatment
#run the gam model
sensitivity_anlys_lin_post_tx_model_log_fixed_lin_time<-lm(log(prop_dead)~ State +
Time_Period_ID:Region +
I(Time_Period_ID^2):Region +
Naloxone_Pharmacy_Yes_Redefined +
Naloxone_Pharmacy_No_Redefined +
Medical_Marijuana_Redefined +
Recreational_Marijuana_Redefined +
GSL_Redefined +
PDMP_Redefined +
Medicaid_Expansion_Redefined +
time_after_tx,
data = sensitivity_anlys_event_study_data_lin_post_tx)
summary(sensitivity_anlys_lin_post_tx_model_log_fixed_lin_time)
##
## Call:
## lm(formula = log(prop_dead) ~ State + Time_Period_ID:Region +
## I(Time_Period_ID^2):Region + Naloxone_Pharmacy_Yes_Redefined +
## Naloxone_Pharmacy_No_Redefined + Medical_Marijuana_Redefined +
## Recreational_Marijuana_Redefined + GSL_Redefined + PDMP_Redefined +
## Medicaid_Expansion_Redefined + time_after_tx, data = sensitivity_anlys_event_study_data_lin_post_tx)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.03249 -0.13280 0.01456 0.15581 1.17227
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.080e+01 5.893e-02 -183.313 < 2e-16 ***
## StateAlaska 3.318e-01 8.851e-02 3.749 0.000183 ***
## StateArizona 5.175e-01 8.518e-02 6.074 1.49e-09 ***
## StateArkansas -5.463e-01 6.756e-02 -8.085 1.08e-15 ***
## StateCalifornia 2.490e-01 9.141e-02 2.724 0.006513 **
## StateColorado 2.392e-01 8.844e-02 2.705 0.006899 **
## StateConnecticut 1.164e-01 8.948e-02 1.301 0.193483
## StateDelaware 1.012e-01 6.911e-02 1.465 0.143128
## StateFlorida 4.647e-01 6.956e-02 6.680 3.11e-11 ***
## StateGeorgia 1.731e-01 7.051e-02 2.455 0.014181 *
## StateHawaii -1.928e-01 8.769e-02 -2.198 0.028040 *
## StateIdaho 9.113e-02 8.584e-02 1.062 0.288569
## StateIllinois 1.185e-01 8.729e-02 1.358 0.174762
## StateIndiana -6.576e-02 8.594e-02 -0.765 0.444253
## StateIowa -7.200e-01 8.589e-02 -8.383 < 2e-16 ***
## StateKansas -3.349e-01 8.529e-02 -3.926 8.94e-05 ***
## StateKentucky 6.487e-01 6.745e-02 9.618 < 2e-16 ***
## StateLouisiana 4.248e-01 6.717e-02 6.324 3.16e-10 ***
## StateMaine -5.379e-02 9.206e-02 -0.584 0.559109
## StateMaryland -1.408e+00 6.933e-02 -20.307 < 2e-16 ***
## StateMassachusetts -1.937e-01 8.946e-02 -2.165 0.030519 *
## StateMichigan -6.126e-02 8.659e-02 -0.707 0.479357
## StateMinnesota -7.856e-01 8.730e-02 -9.000 < 2e-16 ***
## StateMississippi -1.301e-01 6.702e-02 -1.942 0.052301 .
## StateMissouri 7.795e-02 8.694e-02 0.897 0.370048
## StateMontana -7.602e-02 8.751e-02 -0.869 0.385093
## StateNebraska -1.047e+00 8.652e-02 -12.105 < 2e-16 ***
## StateNevada 7.862e-01 8.807e-02 8.927 < 2e-16 ***
## StateNew Hampshire 3.425e-03 8.914e-02 0.038 0.969350
## StateNew Jersey 7.823e-02 9.041e-02 0.865 0.386993
## StateNew Mexico 8.722e-01 8.763e-02 9.953 < 2e-16 ***
## StateNew York -2.386e-01 8.918e-02 -2.676 0.007517 **
## StateNorth Carolina 2.766e-01 6.670e-02 4.148 3.51e-05 ***
## StateNorth Dakota -1.331e+00 8.591e-02 -15.495 < 2e-16 ***
## StateOhio 5.169e-01 8.823e-02 5.859 5.46e-09 ***
## StateOklahoma 4.199e-01 6.712e-02 6.257 4.83e-10 ***
## StateOregon -5.379e-02 8.840e-02 -0.608 0.542933
## StatePennsylvania 6.265e-01 9.247e-02 6.776 1.64e-11 ***
## StateRhode Island -4.734e-01 8.970e-02 -5.278 1.46e-07 ***
## StateSouth Carolina 1.221e-01 6.733e-02 1.813 0.069960 .
## StateSouth Dakota -1.247e+00 8.651e-02 -14.417 < 2e-16 ***
## StateTennessee 4.651e-01 6.626e-02 7.018 3.10e-12 ***
## StateTexas 1.377e-01 6.958e-02 1.979 0.047941 *
## StateUtah 2.581e-01 8.596e-02 3.003 0.002708 **
## StateVermont -3.283e-01 8.947e-02 -3.670 0.000249 ***
## StateVirginia 6.504e-02 6.746e-02 0.964 0.335108
## StateWashington 2.883e-01 8.889e-02 3.243 0.001202 **
## StateWest Virginia 7.370e-01 6.759e-02 10.903 < 2e-16 ***
## StateWisconsin -4.138e-02 8.598e-02 -0.481 0.630407
## StateWyoming 2.680e-01 8.548e-02 3.135 0.001743 **
## Naloxone_Pharmacy_Yes_Redefined 6.423e-02 3.878e-02 1.656 0.097821 .
## Naloxone_Pharmacy_No_Redefined 1.637e-02 3.815e-02 0.429 0.667946
## Medical_Marijuana_Redefined 2.219e-01 3.064e-02 7.243 6.29e-13 ***
## Recreational_Marijuana_Redefined -7.615e-02 4.826e-02 -1.578 0.114733
## GSL_Redefined 6.153e-02 3.118e-02 1.974 0.048566 *
## PDMP_Redefined -1.809e-01 2.458e-02 -7.360 2.70e-13 ***
## Medicaid_Expansion_Redefined 7.524e-02 2.948e-02 2.552 0.010783 *
## time_after_tx -1.539e-02 1.833e-03 -8.398 < 2e-16 ***
## Time_Period_ID:RegionMidwest 8.246e-02 5.098e-03 16.175 < 2e-16 ***
## Time_Period_ID:RegionNortheast 7.030e-02 5.887e-03 11.943 < 2e-16 ***
## Time_Period_ID:RegionSouth 7.655e-02 4.563e-03 16.777 < 2e-16 ***
## Time_Period_ID:RegionWest 6.194e-02 5.042e-03 12.284 < 2e-16 ***
## RegionMidwest:I(Time_Period_ID^2) -7.001e-04 1.283e-04 -5.455 5.52e-08 ***
## RegionNortheast:I(Time_Period_ID^2) -3.013e-04 1.491e-04 -2.021 0.043394 *
## RegionSouth:I(Time_Period_ID^2) -7.078e-04 1.182e-04 -5.986 2.56e-09 ***
## RegionWest:I(Time_Period_ID^2) -6.997e-04 1.304e-04 -5.366 9.00e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2959 on 1934 degrees of freedom
## Multiple R-squared: 0.8424, Adjusted R-squared: 0.8371
## F-statistic: 159.1 on 65 and 1934 DF, p-value: < 2.2e-16
Sandwich Estimator
#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_lin_post_tx_log_fixed_lin_time <-
model.matrix(sensitivity_anlys_lin_post_tx_model_log_fixed_lin_time)
#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_lin_post_tx_log_fixed_lin_time <- coef(sensitivity_anlys_lin_post_tx_model_log_fixed_lin_time)
sensitivity_anlys_lin_post_tx_sd_and_ci_log_fixed_lin_time <-
compute_sd_and_CI((full_df_w_basis_functions_sensitivity_anlys_lin_post_tx_log_fixed_lin_time),
log(sensitivity_anlys_event_study_data$prop_dead),
coefficient_values_sensitivity_anlys_lin_post_tx_log_fixed_lin_time,
p = ncol(full_df_w_basis_functions_sensitivity_anlys_lin_post_tx_log_fixed_lin_time) - 50)
sensitivity_anlys_lin_post_tx_sd_and_ci_log_fixed_lin_time
## lb_coef coef_values ub_coef
## (Intercept) -11.032395000 -1.080239e+01 -1.057239e+01
## StateAlaska 0.016119143 3.318378e-01 6.475564e-01
## StateArizona 0.227468105 5.174508e-01 8.074335e-01
## StateArkansas -0.863335048 -5.462754e-01 -2.292158e-01
## StateCalifornia -0.096482075 2.489906e-01 5.944634e-01
## StateColorado -0.085686088 2.391839e-01 5.640538e-01
## StateConnecticut -0.283445482 1.163972e-01 5.162399e-01
## StateDelaware -0.174119494 1.012298e-01 3.765791e-01
## StateFlorida 0.201896555 4.646892e-01 7.274818e-01
## StateGeorgia -0.091851419 1.731041e-01 4.380595e-01
## StateHawaii -0.511866569 -1.927779e-01 1.263109e-01
## StateIdaho -0.204980318 9.112647e-02 3.872333e-01
## StateIllinois -0.238825672 1.185006e-01 4.758269e-01
## StateIndiana -0.450526951 -6.576075e-02 3.190055e-01
## StateIowa -1.064890868 -7.199910e-01 -3.750911e-01
## StateKansas -0.662085495 -3.348702e-01 -7.654874e-03
## StateKentucky 0.372653717 6.487138e-01 9.247738e-01
## StateLouisiana 0.158121609 4.247528e-01 6.913840e-01
## StateMaine -0.467240181 -5.378727e-02 3.596656e-01
## StateMaryland -1.743134907 -1.407828e+00 -1.072521e+00
## StateMassachusetts -0.757246301 -1.936757e-01 3.698950e-01
## StateMichigan -0.439494246 -6.126213e-02 3.169700e-01
## StateMinnesota -1.141741473 -7.856417e-01 -4.295420e-01
## StateMississippi -0.397788973 -1.301446e-01 1.374998e-01
## StateMissouri -0.272918897 7.795126e-02 4.288214e-01
## StateMontana -0.399997560 -7.602383e-02 2.479499e-01
## StateNebraska -1.389690270 -1.047361e+00 -7.050309e-01
## StateNevada 0.459143786 7.862456e-01 1.113347e+00
## StateNew Hampshire -0.415258494 3.425310e-03 4.221091e-01
## StateNew Jersey -0.324125945 7.822777e-02 4.805815e-01
## StateNew Mexico 0.564941559 8.721992e-01 1.179457e+00
## StateNew York -0.657431192 -2.386233e-01 1.801846e-01
## StateNorth Carolina 0.031729340 2.766402e-01 5.215511e-01
## StateNorth Dakota -1.698467508 -1.331114e+00 -9.637606e-01
## StateOhio 0.143560454 5.169380e-01 8.903155e-01
## StateOklahoma 0.133389278 4.199129e-01 7.064365e-01
## StateOregon -0.375097488 -5.379034e-02 2.675168e-01
## StatePennsylvania 0.203945754 6.265481e-01 1.049150e+00
## StateRhode Island -1.128235679 -4.734177e-01 1.814002e-01
## StateSouth Carolina -0.155208441 1.220894e-01 3.993873e-01
## StateSouth Dakota -1.633177042 -1.247205e+00 -8.612334e-01
## StateTennessee 0.201040214 4.650537e-01 7.290673e-01
## StateTexas -0.120222722 1.377115e-01 3.956457e-01
## StateUtah -0.096631293 2.581386e-01 6.129085e-01
## StateVermont -0.739270544 -3.283355e-01 8.259958e-02
## StateVirginia -0.180958424 6.503933e-02 3.110371e-01
## StateWashington -0.040520561 2.882924e-01 6.171053e-01
## StateWest Virginia 0.421412780 7.369630e-01 1.052513e+00
## StateWisconsin -0.373393925 -4.137857e-02 2.906368e-01
## StateWyoming -0.041192639 2.679994e-01 5.771914e-01
## Naloxone_Pharmacy_Yes_Redefined -0.094785812 6.422503e-02 2.232359e-01
## Naloxone_Pharmacy_No_Redefined -0.139632361 1.636668e-02 1.723657e-01
## Medical_Marijuana_Redefined 0.047111334 2.219211e-01 3.967308e-01
## Recreational_Marijuana_Redefined -0.407922621 -7.614735e-02 2.556279e-01
## GSL_Redefined -0.076199957 6.153342e-02 1.992668e-01
## PDMP_Redefined -0.284064894 -1.808890e-01 -7.771309e-02
## Medicaid_Expansion_Redefined -0.070853004 7.523711e-02 2.213272e-01
## time_after_tx -0.024856265 -1.539237e-02 -5.928480e-03
## Time_Period_ID:RegionMidwest 0.059532671 8.245797e-02 1.053833e-01
## Time_Period_ID:RegionNortheast 0.032505859 7.030490e-02 1.081039e-01
## Time_Period_ID:RegionSouth 0.057796075 7.654703e-02 9.529798e-02
## Time_Period_ID:RegionWest 0.043675612 6.193861e-02 8.020160e-02
## RegionMidwest:I(Time_Period_ID^2) -0.001365405 -7.001224e-04 -3.483966e-05
## RegionNortheast:I(Time_Period_ID^2) -0.001440955 -3.012815e-04 8.383919e-04
## RegionSouth:I(Time_Period_ID^2) -0.001259972 -7.078005e-04 -1.556288e-04
## RegionWest:I(Time_Period_ID^2) -0.001250245 -6.996678e-04 -1.490906e-04
## sd_coef
## (Intercept) 0.1173490481
## StateAlaska 0.1610809373
## StateArizona 0.1479503602
## StateArkansas 0.1617651094
## StateCalifornia 0.1762615891
## StateColorado 0.1657499715
## StateConnecticut 0.2040013847
## StateDelaware 0.1404843224
## StateFlorida 0.1340778593
## StateGeorgia 0.1351813649
## StateHawaii 0.1628003639
## StateIdaho 0.1510748900
## StateIllinois 0.1823093222
## StateIndiana 0.1963092883
## StateIowa 0.1759693219
## StateKansas 0.1669465869
## StateKentucky 0.1408469601
## StateLouisiana 0.1360363128
## StateMaine 0.2109453620
## StateMaryland 0.1710749459
## StateMassachusetts 0.2875360375
## StateMichigan 0.1929755715
## StateMinnesota 0.1816835457
## StateMississippi 0.1365532677
## StateMissouri 0.1790153884
## StateMontana 0.1652927169
## StateNebraska 0.1746580152
## StateNevada 0.1668886967
## StateNew Hampshire 0.2136141855
## StateNew Jersey 0.2052825074
## StateNew Mexico 0.1567640963
## StateNew York 0.2136775066
## StateNorth Carolina 0.1249545377
## StateNorth Dakota 0.1874252275
## StateOhio 0.1904987489
## StateOklahoma 0.1461855086
## StateOregon 0.1639322162
## StatePennsylvania 0.2156134313
## StateRhode Island 0.3340907852
## StateSouth Carolina 0.1414785137
## StateSouth Dakota 0.1969244111
## StateTennessee 0.1347007823
## StateTexas 0.1315990905
## StateUtah 0.1810050386
## StateVermont 0.2096607458
## StateVirginia 0.1255090597
## StateWashington 0.1677617090
## StateWest Virginia 0.1609949936
## StateWisconsin 0.1693955894
## StateWyoming 0.1577510213
## Naloxone_Pharmacy_Yes_Redefined 0.0811279823
## Naloxone_Pharmacy_No_Redefined 0.0795913458
## Medical_Marijuana_Redefined 0.0891886370
## Recreational_Marijuana_Redefined 0.1692730984
## GSL_Redefined 0.0702721302
## PDMP_Redefined 0.0526407657
## Medicaid_Expansion_Redefined 0.0745357728
## time_after_tx 0.0048285167
## Time_Period_ID:RegionMidwest 0.0116965829
## Time_Period_ID:RegionNortheast 0.0192852249
## Time_Period_ID:RegionSouth 0.0095668113
## Time_Period_ID:RegionWest 0.0093178545
## RegionMidwest:I(Time_Period_ID^2) 0.0003394300
## RegionNortheast:I(Time_Period_ID^2) 0.0005814660
## RegionSouth:I(Time_Period_ID^2) 0.0002817203
## RegionWest:I(Time_Period_ID^2) 0.0002809067